Rouben Rostamian

MaplePrimes Activity


These are replies submitted by Rouben Rostamian

@Ahmed111 As Carl has pointed out, the trouble in Maple 18 may be due to "with(Physics)".  But that package is not needed in Linearize.mw.   Remove and try it again.

@Carl Love I misunderstood the question.  Then perhaps this is what is wanted:

NULL

4*c^2*((4/3)*c^2*(exp(((1/3)*I)*3^(1/2)*t))^2*(1+epsilon[2])^4*(exp(-((1/3)*I)*3^(1/2)*t))^2+8*c*(-(1/12)*3^(1/2)*(1+epsilon[2])^2*(diff(diff(epsilon[1], t), x))+(1+epsilon[1])^2*c*((diff(epsilon[2], t))^2+(1/3)*(1+epsilon[2])^2))*exp(((1/3)*I)*3^(1/2)*t)*exp(-((1/3)*I)*3^(1/2)*t)+(1/4)*(diff(diff(epsilon[1], t), x))^2+(1+epsilon[1])^2*(c*(diff(epsilon[1], t))-2)*(c*(diff(epsilon[1], t))+2)) = 0

indets(Eq1, function)

{epsilon[1], epsilon[2], exp(-((1/3)*I)*3^(1/2)*t), exp(((1/3)*I)*3^(1/2)*t), Physics:-diff(epsilon[1], t), Physics:-diff(epsilon[2], t), Physics:-diff(Physics:-diff(epsilon[1], t), x)}

In Eq1 replace diff(`ε`[1], t, x) by the symbol e__1tx, etc., linearize with respect to those symbols,

and then restore the symbols to their original meanings:

subs(diff(`ε`[1], t, x) = e__1tx, diff(`ε`[1], t) = e__1t, `ε`[1] = e__1, diff(`ε`[2], t) = e__2t, `ε`[2] = e__2, lhs(Eq1)); mtaylor(%, [e__1, e__1t, e__1tx, e__2, e__2t], 2); subs(e__1 = `ε`[1], e__2 = `ε`[2], e__1tx = diff(`ε`[1], t, x), %); simplify(%); collect(%, [`ε`[1], `ε`[2], diff(`ε`[1], t, x)]) = 0

-(8/3)*c^2*(-8*c^2+12)*epsilon[1]+(128/3)*c^4*epsilon[2]-(8/3)*c^3*3^(1/2)*(diff(diff(epsilon[1], t), x))-(8/3)*c^2*(-6*c^2+6) = 0

NULL


Download: Lineaize.mw

@Earl The opening paragraph of the Wikipedia page that you referred to in your original message, begins with:

      In geometry, a geodesic is commonly a curve representing
      in some sense the shortest path between two points in a surface.

Note the qualifier "in some sense" there; it is not making an absolute statement that a geodesic is the shortest path!

Technically, a geodesic curve on a surface is defined to be the generalization, in a very precise technical sense, of a straight line in the plane. For instance, a great circle on a sphere is a geodesic; it's the closest thing to a straight line that lies on a sphere. There is no appeal here to "two points" or "shortest distance".

The shortest length property of a geodesic is a consequence (i.e., it is proved as a theorem) of the "straight line" definition alluded to above. It holds under certain circumstances but it is not always valid without qualifications.

Have a look at the picture of the green cone in my previous message. The shortest path between the two orange points is the obvious little arc (not drawn) that connects those points. However, look at the red curve which also connects those two points. Imagine this as a real physical cone and the red curve as a (loose) rope that winds around the cone as shown, and goes through those two points. What would happen if you pulled that rope real tight? You will be minimizing the rope's length! The rope will take the shape as drawn. So yes, that shape is also a "shortest distance" between those two points. It is the shortest among all curves that wind around the cone once. It is shortest because if you try to pull any harder, the rope will break; you cannot make it any shorter.

This should clarify my statement that there may be multiple geodesics between two curves on a surface.  In that connection, have a look at the red and cyan geodesics on the animated torus in my earlier reply.

 

@Earl Okay, here it is: A geodesic on a cone

Download worksheet: geodesic-on-cone.mw

 

@Earl Yes, there is an idea there which I had not thought about, and which can be useful in some situatios.   Specifically, if the surface is parametrized such that geodesics are single-valued functions of one of the surface's parameters, then we may characterize those geodesics as solutions of boundary values problems of a 2nd order ODE obtained through the Euler-Lagrange equations. This works particularly well with toruses as in the illustrated answer which I am going to post next.  It should work in the case of some other interesting surfaces but I haven't tried.

@Earl I don't see an easy way to modify the code to do what you have asked.

There is some literature on the subject.  Perhaps a good way is to Google for "how to calculate the geodesic going through two given points".  I just did that and obtained two promising articles.

  1. This one appears to have been written by undergraduates.  Their methods seem to work but are computationally inefficient.
  2. This one appears to be more sophisticated. I haven't looked at the details but it seems to be worth a look.

I may give this question a try when I have some more time but not now.

@ecterrab That works!. Thanks!

PS: In the first of the two maplinit lines that you have provided, the "=" should be ":=".  

@ecterrab Thanks for the quick fix, as always!

Edgardo, that's a very nice enhancement.

Would it be possible to let users make the subscripted variables the default by setting some kind of environment variable in mapleinit?

@vv Yes, pdsolve() does return the correct general solution.  Something goes wrong when it tries to apply the initial condition.

Here is a possible enhancement to Maple pdsolve().  In the same way that dsolve() offers an implicit option. it would be helpful if pdsolve() also offered that option.  Then the solution of the initial value problem ut + u ux = 0, u(x,0) = f(x) would be expressed as f(x − ut) = u which is more pleasant than the RootOf expressions to look at. 

@Earl That looks good.  Good job!

 

@Preben Alsholm I like that.  Very nice!

@acer Thanks for getting to the bottom of this.  Now it's clear to me why D[1](U)(0,t) does not return a value .

So now we have two ways for calculating the boundary flux.  One way is through the boundary_flux() function which I described earlier.  Another way is to calculate −D[1](U,h,t) where h=Float(1,−Digits/2).  That actually calculates the flux at y=h, but since h is so small, the value calculated here is practically the same as the flux at the boundary.

As long as we are at it, let me point out that a more accurate version of the boundary_flux() function may be obtained by replacing the 1st order finite difference by a 2nd order finite difference, as in:

h := Float(1,-Digits/2);
boundary_flux := t -> - ( -3/2*U(0, t) + 2*U(h,t) - 1/2*U(2*h,t) ) / h;

This would be my preferred method of calculating the boundary flux if I had a need for it in my work.

@Moqifang I don't know what prevents the evaluation of the y derivative at the boundary.  It's not a version issue, since it doesn't work on my Maple 2022 either.  Nevertheless, there is an easy workaround as we see in the following fragment corresponding to your screenshot:

vals := sol1:-value(u(y,t), output=listprocedure);

[y = proc () option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; evalf(args[1]) end proc, t = proc () option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; evalf(args[2]) end proc, u(y, t) = proc () local tv, xv, solnproc, stype, ndsol, vals; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; Digits := trunc(evalhf(Digits)); solnproc := proc (tv, xv) local INFO, errest, nd, dvars, dary, daryt, daryx, vals, msg, i, j; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; table( [( "soln_procedures" ) = array( 1 .. 1, [( 1 ) = (36893628355780618476)  ] ) ] ) INFO := table( [( "t0" ) = 0, ( "eqnords" ) = [[2, 1]], ( "minspcpoints" ) = 4, ( "norigdepvars" ) = 1, ( "maxords" ) = [2, 1], ( "depshift" ) = [1], ( "solmat_v" ) = Vector(606, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0, (102) = .0, (103) = .0, (104) = .0, (105) = .0, (106) = .0, (107) = .0, (108) = .0, (109) = .0, (110) = .0, (111) = .0, (112) = .0, (113) = .0, (114) = .0, (115) = .0, (116) = .0, (117) = .0, (118) = .0, (119) = .0, (120) = .0, (121) = .0, (122) = .0, (123) = .0, (124) = .0, (125) = .0, (126) = .0, (127) = .0, (128) = .0, (129) = .0, (130) = .0, (131) = .0, (132) = .0, (133) = .0, (134) = .0, (135) = .0, (136) = .0, (137) = .0, (138) = .0, (139) = .0, (140) = .0, (141) = .0, (142) = .0, (143) = .0, (144) = .0, (145) = .0, (146) = .0, (147) = .0, (148) = .0, (149) = .0, (150) = .0, (151) = .0, (152) = .0, (153) = .0, (154) = .0, (155) = .0, (156) = .0, (157) = .0, (158) = .0, (159) = .0, (160) = .0, (161) = .0, (162) = .0, (163) = .0, (164) = .0, (165) = .0, (166) = .0, (167) = .0, (168) = .0, (169) = .0, (170) = .0, (171) = .0, (172) = .0, (173) = .0, (174) = .0, (175) = .0, (176) = .0, (177) = .0, (178) = .0, (179) = .0, (180) = .0, (181) = .0, (182) = .0, (183) = .0, (184) = .0, (185) = .0, (186) = .0, (187) = .0, (188) = .0, (189) = .0, (190) = .0, (191) = .0, (192) = .0, (193) = .0, (194) = .0, (195) = .0, (196) = .0, (197) = .0, (198) = .0, (199) = .0, (200) = .0, (201) = .0, (202) = .0, (203) = .0, (204) = .0, (205) = .0, (206) = .0, (207) = .0, (208) = .0, (209) = .0, (210) = .0, (211) = .0, (212) = .0, (213) = .0, (214) = .0, (215) = .0, (216) = .0, (217) = .0, (218) = .0, (219) = .0, (220) = .0, (221) = .0, (222) = .0, (223) = .0, (224) = .0, (225) = .0, (226) = .0, (227) = .0, (228) = .0, (229) = .0, (230) = .0, (231) = .0, (232) = .0, (233) = .0, (234) = .0, (235) = .0, (236) = .0, (237) = .0, (238) = .0, (239) = .0, (240) = .0, (241) = .0, (242) = .0, (243) = .0, (244) = .0, (245) = .0, (246) = .0, (247) = .0, (248) = .0, (249) = .0, (250) = .0, (251) = .0, (252) = .0, (253) = .0, (254) = .0, (255) = .0, (256) = .0, (257) = .0, (258) = .0, (259) = .0, (260) = .0, (261) = .0, (262) = .0, (263) = .0, (264) = .0, (265) = .0, (266) = .0, (267) = .0, (268) = .0, (269) = .0, (270) = .0, (271) = .0, (272) = .0, (273) = .0, (274) = .0, (275) = .0, (276) = .0, (277) = .0, (278) = .0, (279) = .0, (280) = .0, (281) = .0, (282) = .0, (283) = .0, (284) = .0, (285) = .0, (286) = .0, (287) = .0, (288) = .0, (289) = .0, (290) = .0, (291) = .0, (292) = .0, (293) = .0, (294) = .0, (295) = .0, (296) = .0, (297) = .0, (298) = .0, (299) = .0, (300) = .0, (301) = .0, (302) = .0, (303) = .0, (304) = .0, (305) = .0, (306) = .0, (307) = .0, (308) = .0, (309) = .0, (310) = .0, (311) = .0, (312) = .0, (313) = .0, (314) = .0, (315) = .0, (316) = .0, (317) = .0, (318) = .0, (319) = .0, (320) = .0, (321) = .0, (322) = .0, (323) = .0, (324) = .0, (325) = .0, (326) = .0, (327) = .0, (328) = .0, (329) = .0, (330) = .0, (331) = .0, (332) = .0, (333) = .0, (334) = .0, (335) = .0, (336) = .0, (337) = .0, (338) = .0, (339) = .0, (340) = .0, (341) = .0, (342) = .0, (343) = .0, (344) = .0, (345) = .0, (346) = .0, (347) = .0, (348) = .0, (349) = .0, (350) = .0, (351) = .0, (352) = .0, (353) = .0, (354) = .0, (355) = .0, (356) = .0, (357) = .0, (358) = .0, (359) = .0, (360) = .0, (361) = .0, (362) = .0, (363) = .0, (364) = .0, (365) = .0, (366) = .0, (367) = .0, (368) = .0, (369) = .0, (370) = .0, (371) = .0, (372) = .0, (373) = .0, (374) = .0, (375) = .0, (376) = .0, (377) = .0, (378) = .0, (379) = .0, (380) = .0, (381) = .0, (382) = .0, (383) = .0, (384) = .0, (385) = .0, (386) = .0, (387) = .0, (388) = .0, (389) = .0, (390) = .0, (391) = .0, (392) = .0, (393) = .0, (394) = .0, (395) = .0, (396) = .0, (397) = .0, (398) = .0, (399) = .0, (400) = .0, (401) = .0, (402) = .0, (403) = .0, (404) = .0, (405) = .0, (406) = .0, (407) = .0, (408) = .0, (409) = .0, (410) = .0, (411) = .0, (412) = .0, (413) = .0, (414) = .0, (415) = .0, (416) = .0, (417) = .0, (418) = .0, (419) = .0, (420) = .0, (421) = .0, (422) = .0, (423) = .0, (424) = .0, (425) = .0, (426) = .0, (427) = .0, (428) = .0, (429) = .0, (430) = .0, (431) = .0, (432) = .0, (433) = .0, (434) = .0, (435) = .0, (436) = .0, (437) = .0, (438) = .0, (439) = .0, (440) = .0, (441) = .0, (442) = .0, (443) = .0, (444) = .0, (445) = .0, (446) = .0, (447) = .0, (448) = .0, (449) = .0, (450) = .0, (451) = .0, (452) = .0, (453) = .0, (454) = .0, (455) = .0, (456) = .0, (457) = .0, (458) = .0, (459) = .0, (460) = .0, (461) = .0, (462) = .0, (463) = .0, (464) = .0, (465) = .0, (466) = .0, (467) = .0, (468) = .0, (469) = .0, (470) = .0, (471) = .0, (472) = .0, (473) = .0, (474) = .0, (475) = .0, (476) = .0, (477) = .0, (478) = .0, (479) = .0, (480) = .0, (481) = .0, (482) = .0, (483) = .0, (484) = .0, (485) = .0, (486) = .0, (487) = .0, (488) = .0, (489) = .0, (490) = .0, (491) = .0, (492) = .0, (493) = .0, (494) = .0, (495) = .0, (496) = .0, (497) = .0, (498) = .0, (499) = .0, (500) = .0, (501) = .0, (502) = .0, (503) = .0, (504) = .0, (505) = .0, (506) = .0, (507) = .0, (508) = .0, (509) = .0, (510) = .0, (511) = .0, (512) = .0, (513) = .0, (514) = .0, (515) = .0, (516) = .0, (517) = .0, (518) = .0, (519) = .0, (520) = .0, (521) = .0, (522) = .0, (523) = .0, (524) = .0, (525) = .0, (526) = .0, (527) = .0, (528) = .0, (529) = .0, (530) = .0, (531) = .0, (532) = .0, (533) = .0, (534) = .0, (535) = .0, (536) = .0, (537) = .0, (538) = .0, (539) = .0, (540) = .0, (541) = .0, (542) = .0, (543) = .0, (544) = .0, (545) = .0, (546) = .0, (547) = .0, (548) = .0, (549) = .0, (550) = .0, (551) = .0, (552) = .0, (553) = .0, (554) = .0, (555) = .0, (556) = .0, (557) = .0, (558) = .0, (559) = .0, (560) = .0, (561) = .0, (562) = .0, (563) = .0, (564) = .0, (565) = .0, (566) = .0, (567) = .0, (568) = .0, (569) = .0, (570) = .0, (571) = .0, (572) = .0, (573) = .0, (574) = .0, (575) = .0, (576) = .0, (577) = .0, (578) = .0, (579) = .0, (580) = .0, (581) = .0, (582) = .0, (583) = .0, (584) = .0, (585) = .0, (586) = .0, (587) = .0, (588) = .0, (589) = .0, (590) = .0, (591) = .0, (592) = .0, (593) = .0, (594) = .0, (595) = .0, (596) = .0, (597) = .0, (598) = .0, (599) = .0, (600) = .0, (601) = .0, (602) = .0, (603) = .0, (604) = .0, (605) = .0, (606) = .0}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(101, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (42, 1) = .0, (42, 2) = .0, (42, 3) = .0, (42, 4) = .0, (42, 5) = .0, (42, 6) = .0, (43, 1) = .0, (43, 2) = .0, (43, 3) = .0, (43, 4) = .0, (43, 5) = .0, (43, 6) = .0, (44, 1) = .0, (44, 2) = .0, (44, 3) = .0, (44, 4) = .0, (44, 5) = .0, (44, 6) = .0, (45, 1) = .0, (45, 2) = .0, (45, 3) = .0, (45, 4) = .0, (45, 5) = .0, (45, 6) = .0, (46, 1) = .0, (46, 2) = .0, (46, 3) = .0, (46, 4) = .0, (46, 5) = .0, (46, 6) = .0, (47, 1) = .0, (47, 2) = .0, (47, 3) = .0, (47, 4) = .0, (47, 5) = .0, (47, 6) = .0, (48, 1) = .0, (48, 2) = .0, (48, 3) = .0, (48, 4) = .0, (48, 5) = .0, (48, 6) = .0, (49, 1) = .0, (49, 2) = .0, (49, 3) = .0, (49, 4) = .0, (49, 5) = .0, (49, 6) = .0, (50, 1) = .0, (50, 2) = .0, (50, 3) = .0, (50, 4) = .0, (50, 5) = .0, (50, 6) = .0, (51, 1) = .0, (51, 2) = .0, (51, 3) = .0, (51, 4) = .0, (51, 5) = .0, (51, 6) = .0, (52, 1) = .0, (52, 2) = .0, (52, 3) = .0, (52, 4) = .0, (52, 5) = .0, (52, 6) = .0, (53, 1) = .0, (53, 2) = .0, (53, 3) = .0, (53, 4) = .0, (53, 5) = .0, (53, 6) = .0, (54, 1) = .0, (54, 2) = .0, (54, 3) = .0, (54, 4) = .0, (54, 5) = .0, (54, 6) = .0, (55, 1) = .0, (55, 2) = .0, (55, 3) = .0, (55, 4) = .0, (55, 5) = .0, (55, 6) = .0, (56, 1) = .0, (56, 2) = .0, (56, 3) = .0, (56, 4) = .0, (56, 5) = .0, (56, 6) = .0, (57, 1) = .0, (57, 2) = .0, (57, 3) = .0, (57, 4) = .0, (57, 5) = .0, (57, 6) = .0, (58, 1) = .0, (58, 2) = .0, (58, 3) = .0, (58, 4) = .0, (58, 5) = .0, (58, 6) = .0, (59, 1) = .0, (59, 2) = .0, (59, 3) = .0, (59, 4) = .0, (59, 5) = .0, (59, 6) = .0, (60, 1) = .0, (60, 2) = .0, (60, 3) = .0, (60, 4) = .0, (60, 5) = .0, (60, 6) = .0, (61, 1) = .0, (61, 2) = .0, (61, 3) = .0, (61, 4) = .0, (61, 5) = .0, (61, 6) = .0, (62, 1) = .0, (62, 2) = .0, (62, 3) = .0, (62, 4) = .0, (62, 5) = .0, (62, 6) = .0, (63, 1) = .0, (63, 2) = .0, (63, 3) = .0, (63, 4) = .0, (63, 5) = .0, (63, 6) = .0, (64, 1) = .0, (64, 2) = .0, (64, 3) = .0, (64, 4) = .0, (64, 5) = .0, (64, 6) = .0, (65, 1) = .0, (65, 2) = .0, (65, 3) = .0, (65, 4) = .0, (65, 5) = .0, (65, 6) = .0, (66, 1) = .0, (66, 2) = .0, (66, 3) = .0, (66, 4) = .0, (66, 5) = .0, (66, 6) = .0, (67, 1) = .0, (67, 2) = .0, (67, 3) = .0, (67, 4) = .0, (67, 5) = .0, (67, 6) = .0, (68, 1) = .0, (68, 2) = .0, (68, 3) = .0, (68, 4) = .0, (68, 5) = .0, (68, 6) = .0, (69, 1) = .0, (69, 2) = .0, (69, 3) = .0, (69, 4) = .0, (69, 5) = .0, (69, 6) = .0, (70, 1) = .0, (70, 2) = .0, (70, 3) = .0, (70, 4) = .0, (70, 5) = .0, (70, 6) = .0, (71, 1) = .0, (71, 2) = .0, (71, 3) = .0, (71, 4) = .0, (71, 5) = .0, (71, 6) = .0, (72, 1) = .0, (72, 2) = .0, (72, 3) = .0, (72, 4) = .0, (72, 5) = .0, (72, 6) = .0, (73, 1) = .0, (73, 2) = .0, (73, 3) = .0, (73, 4) = .0, (73, 5) = .0, (73, 6) = .0, (74, 1) = .0, (74, 2) = .0, (74, 3) = .0, (74, 4) = .0, (74, 5) = .0, (74, 6) = .0, (75, 1) = .0, (75, 2) = .0, (75, 3) = .0, (75, 4) = .0, (75, 5) = .0, (75, 6) = .0, (76, 1) = .0, (76, 2) = .0, (76, 3) = .0, (76, 4) = .0, (76, 5) = .0, (76, 6) = .0, (77, 1) = .0, (77, 2) = .0, (77, 3) = .0, (77, 4) = .0, (77, 5) = .0, (77, 6) = .0, (78, 1) = .0, (78, 2) = .0, (78, 3) = .0, (78, 4) = .0, (78, 5) = .0, (78, 6) = .0, (79, 1) = .0, (79, 2) = .0, (79, 3) = .0, (79, 4) = .0, (79, 5) = .0, (79, 6) = .0, (80, 1) = .0, (80, 2) = .0, (80, 3) = .0, (80, 4) = .0, (80, 5) = .0, (80, 6) = .0, (81, 1) = .0, (81, 2) = .0, (81, 3) = .0, (81, 4) = .0, (81, 5) = .0, (81, 6) = .0, (82, 1) = .0, (82, 2) = .0, (82, 3) = .0, (82, 4) = .0, (82, 5) = .0, (82, 6) = .0, (83, 1) = .0, (83, 2) = .0, (83, 3) = .0, (83, 4) = .0, (83, 5) = .0, (83, 6) = .0, (84, 1) = .0, (84, 2) = .0, (84, 3) = .0, (84, 4) = .0, (84, 5) = .0, (84, 6) = .0, (85, 1) = .0, (85, 2) = .0, (85, 3) = .0, (85, 4) = .0, (85, 5) = .0, (85, 6) = .0, (86, 1) = .0, (86, 2) = .0, (86, 3) = .0, (86, 4) = .0, (86, 5) = .0, (86, 6) = .0, (87, 1) = .0, (87, 2) = .0, (87, 3) = .0, (87, 4) = .0, (87, 5) = .0, (87, 6) = .0, (88, 1) = .0, (88, 2) = .0, (88, 3) = .0, (88, 4) = .0, (88, 5) = .0, (88, 6) = .0, (89, 1) = .0, (89, 2) = .0, (89, 3) = .0, (89, 4) = .0, (89, 5) = .0, (89, 6) = .0, (90, 1) = .0, (90, 2) = .0, (90, 3) = .0, (90, 4) = .0, (90, 5) = .0, (90, 6) = .0, (91, 1) = .0, (91, 2) = .0, (91, 3) = .0, (91, 4) = .0, (91, 5) = .0, (91, 6) = .0, (92, 1) = .0, (92, 2) = .0, (92, 3) = .0, (92, 4) = .0, (92, 5) = .0, (92, 6) = .0, (93, 1) = .0, (93, 2) = .0, (93, 3) = .0, (93, 4) = .0, (93, 5) = .0, (93, 6) = .0, (94, 1) = .0, (94, 2) = .0, (94, 3) = .0, (94, 4) = .0, (94, 5) = .0, (94, 6) = .0, (95, 1) = .0, (95, 2) = .0, (95, 3) = .0, (95, 4) = .0, (95, 5) = .0, (95, 6) = .0, (96, 1) = .0, (96, 2) = .0, (96, 3) = .0, (96, 4) = .0, (96, 5) = .0, (96, 6) = .0, (97, 1) = .0, (97, 2) = .0, (97, 3) = .0, (97, 4) = .0, (97, 5) = .0, (97, 6) = .0, (98, 1) = .0, (98, 2) = .0, (98, 3) = .0, (98, 4) = .0, (98, 5) = .0, (98, 6) = .0, (99, 1) = .0, (99, 2) = .0, (99, 3) = .0, (99, 4) = .0, (99, 5) = .0, (99, 6) = .0, (100, 1) = .0, (100, 2) = .0, (100, 3) = .0, (100, 4) = .0, (100, 5) = .0, (100, 6) = .0, (101, 1) = .0, (101, 2) = .0, (101, 3) = .0, (101, 4) = .0, (101, 5) = .0, (101, 6) = .0}, datatype = float[8], order = C_order))]), ( "spacevar" ) = y, ( "timeidx" ) = 2, ( "depords" ) = [[2, 1]], ( "theta" ) = 1/2, ( "erroraccum" ) = true, ( "spacepts" ) = 101, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, xi; _s2 := 1/k; _s3 := (1/2)/h^2; vec[1] := cos(t+k); vec[n] := 0; for xi from 2 to n-1 do _s1 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := _s3*_s1+_s2*vp[xi] end do end proc, ( "rightwidth" ) = 0, ( "ICS" ) = [0], ( "matrixhf" ) = true, ( "IBC" ) = b, ( "bandwidth" ) = [1, 2], ( "pts", y ) = [0, 10], ( "dependson" ) = [{1}], ( "vectorhf" ) = true, ( "spaceidx" ) = 1, ( "banded" ) = true, ( "solvec4" ) = 0, ( "indepvars" ) = [y, t], ( "spacestep" ) = .100000000000000, ( "linear" ) = true, ( "timestep" ) = 0.100000000000000e-1, ( "mixed" ) = false, ( "method" ) = theta, ( "solmat_is" ) = 0, ( "solution" ) = Array(1..3, 1..101, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (1, 22, 1) = .0, (1, 23, 1) = .0, (1, 24, 1) = .0, (1, 25, 1) = .0, (1, 26, 1) = .0, (1, 27, 1) = .0, (1, 28, 1) = .0, (1, 29, 1) = .0, (1, 30, 1) = .0, (1, 31, 1) = .0, (1, 32, 1) = .0, (1, 33, 1) = .0, (1, 34, 1) = .0, (1, 35, 1) = .0, (1, 36, 1) = .0, (1, 37, 1) = .0, (1, 38, 1) = .0, (1, 39, 1) = .0, (1, 40, 1) = .0, (1, 41, 1) = .0, (1, 42, 1) = .0, (1, 43, 1) = .0, (1, 44, 1) = .0, (1, 45, 1) = .0, (1, 46, 1) = .0, (1, 47, 1) = .0, (1, 48, 1) = .0, (1, 49, 1) = .0, (1, 50, 1) = .0, (1, 51, 1) = .0, (1, 52, 1) = .0, (1, 53, 1) = .0, (1, 54, 1) = .0, (1, 55, 1) = .0, (1, 56, 1) = .0, (1, 57, 1) = .0, (1, 58, 1) = .0, (1, 59, 1) = .0, (1, 60, 1) = .0, (1, 61, 1) = .0, (1, 62, 1) = .0, (1, 63, 1) = .0, (1, 64, 1) = .0, (1, 65, 1) = .0, (1, 66, 1) = .0, (1, 67, 1) = .0, (1, 68, 1) = .0, (1, 69, 1) = .0, (1, 70, 1) = .0, (1, 71, 1) = .0, (1, 72, 1) = .0, (1, 73, 1) = .0, (1, 74, 1) = .0, (1, 75, 1) = .0, (1, 76, 1) = .0, (1, 77, 1) = .0, (1, 78, 1) = .0, (1, 79, 1) = .0, (1, 80, 1) = .0, (1, 81, 1) = .0, (1, 82, 1) = .0, (1, 83, 1) = .0, (1, 84, 1) = .0, (1, 85, 1) = .0, (1, 86, 1) = .0, (1, 87, 1) = .0, (1, 88, 1) = .0, (1, 89, 1) = .0, (1, 90, 1) = .0, (1, 91, 1) = .0, (1, 92, 1) = .0, (1, 93, 1) = .0, (1, 94, 1) = .0, (1, 95, 1) = .0, (1, 96, 1) = .0, (1, 97, 1) = .0, (1, 98, 1) = .0, (1, 99, 1) = .0, (1, 100, 1) = .0, (1, 101, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (2, 22, 1) = .0, (2, 23, 1) = .0, (2, 24, 1) = .0, (2, 25, 1) = .0, (2, 26, 1) = .0, (2, 27, 1) = .0, (2, 28, 1) = .0, (2, 29, 1) = .0, (2, 30, 1) = .0, (2, 31, 1) = .0, (2, 32, 1) = .0, (2, 33, 1) = .0, (2, 34, 1) = .0, (2, 35, 1) = .0, (2, 36, 1) = .0, (2, 37, 1) = .0, (2, 38, 1) = .0, (2, 39, 1) = .0, (2, 40, 1) = .0, (2, 41, 1) = .0, (2, 42, 1) = .0, (2, 43, 1) = .0, (2, 44, 1) = .0, (2, 45, 1) = .0, (2, 46, 1) = .0, (2, 47, 1) = .0, (2, 48, 1) = .0, (2, 49, 1) = .0, (2, 50, 1) = .0, (2, 51, 1) = .0, (2, 52, 1) = .0, (2, 53, 1) = .0, (2, 54, 1) = .0, (2, 55, 1) = .0, (2, 56, 1) = .0, (2, 57, 1) = .0, (2, 58, 1) = .0, (2, 59, 1) = .0, (2, 60, 1) = .0, (2, 61, 1) = .0, (2, 62, 1) = .0, (2, 63, 1) = .0, (2, 64, 1) = .0, (2, 65, 1) = .0, (2, 66, 1) = .0, (2, 67, 1) = .0, (2, 68, 1) = .0, (2, 69, 1) = .0, (2, 70, 1) = .0, (2, 71, 1) = .0, (2, 72, 1) = .0, (2, 73, 1) = .0, (2, 74, 1) = .0, (2, 75, 1) = .0, (2, 76, 1) = .0, (2, 77, 1) = .0, (2, 78, 1) = .0, (2, 79, 1) = .0, (2, 80, 1) = .0, (2, 81, 1) = .0, (2, 82, 1) = .0, (2, 83, 1) = .0, (2, 84, 1) = .0, (2, 85, 1) = .0, (2, 86, 1) = .0, (2, 87, 1) = .0, (2, 88, 1) = .0, (2, 89, 1) = .0, (2, 90, 1) = .0, (2, 91, 1) = .0, (2, 92, 1) = .0, (2, 93, 1) = .0, (2, 94, 1) = .0, (2, 95, 1) = .0, (2, 96, 1) = .0, (2, 97, 1) = .0, (2, 98, 1) = .0, (2, 99, 1) = .0, (2, 100, 1) = .0, (2, 101, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0, (3, 22, 1) = .0, (3, 23, 1) = .0, (3, 24, 1) = .0, (3, 25, 1) = .0, (3, 26, 1) = .0, (3, 27, 1) = .0, (3, 28, 1) = .0, (3, 29, 1) = .0, (3, 30, 1) = .0, (3, 31, 1) = .0, (3, 32, 1) = .0, (3, 33, 1) = .0, (3, 34, 1) = .0, (3, 35, 1) = .0, (3, 36, 1) = .0, (3, 37, 1) = .0, (3, 38, 1) = .0, (3, 39, 1) = .0, (3, 40, 1) = .0, (3, 41, 1) = .0, (3, 42, 1) = .0, (3, 43, 1) = .0, (3, 44, 1) = .0, (3, 45, 1) = .0, (3, 46, 1) = .0, (3, 47, 1) = .0, (3, 48, 1) = .0, (3, 49, 1) = .0, (3, 50, 1) = .0, (3, 51, 1) = .0, (3, 52, 1) = .0, (3, 53, 1) = .0, (3, 54, 1) = .0, (3, 55, 1) = .0, (3, 56, 1) = .0, (3, 57, 1) = .0, (3, 58, 1) = .0, (3, 59, 1) = .0, (3, 60, 1) = .0, (3, 61, 1) = .0, (3, 62, 1) = .0, (3, 63, 1) = .0, (3, 64, 1) = .0, (3, 65, 1) = .0, (3, 66, 1) = .0, (3, 67, 1) = .0, (3, 68, 1) = .0, (3, 69, 1) = .0, (3, 70, 1) = .0, (3, 71, 1) = .0, (3, 72, 1) = .0, (3, 73, 1) = .0, (3, 74, 1) = .0, (3, 75, 1) = .0, (3, 76, 1) = .0, (3, 77, 1) = .0, (3, 78, 1) = .0, (3, 79, 1) = .0, (3, 80, 1) = .0, (3, 81, 1) = .0, (3, 82, 1) = .0, (3, 83, 1) = .0, (3, 84, 1) = .0, (3, 85, 1) = .0, (3, 86, 1) = .0, (3, 87, 1) = .0, (3, 88, 1) = .0, (3, 89, 1) = .0, (3, 90, 1) = .0, (3, 91, 1) = .0, (3, 92, 1) = .0, (3, 93, 1) = .0, (3, 94, 1) = .0, (3, 95, 1) = .0, (3, 96, 1) = .0, (3, 97, 1) = .0, (3, 98, 1) = .0, (3, 99, 1) = .0, (3, 100, 1) = .0, (3, 101, 1) = .0}, datatype = float[8], order = C_order), ( "multidep" ) = [false, false], ( "solmatrix" ) = Matrix(101, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (42, 1) = .0, (42, 2) = .0, (42, 3) = .0, (42, 4) = .0, (42, 5) = .0, (42, 6) = .0, (43, 1) = .0, (43, 2) = .0, (43, 3) = .0, (43, 4) = .0, (43, 5) = .0, (43, 6) = .0, (44, 1) = .0, (44, 2) = .0, (44, 3) = .0, (44, 4) = .0, (44, 5) = .0, (44, 6) = .0, (45, 1) = .0, (45, 2) = .0, (45, 3) = .0, (45, 4) = .0, (45, 5) = .0, (45, 6) = .0, (46, 1) = .0, (46, 2) = .0, (46, 3) = .0, (46, 4) = .0, (46, 5) = .0, (46, 6) = .0, (47, 1) = .0, (47, 2) = .0, (47, 3) = .0, (47, 4) = .0, (47, 5) = .0, (47, 6) = .0, (48, 1) = .0, (48, 2) = .0, (48, 3) = .0, (48, 4) = .0, (48, 5) = .0, (48, 6) = .0, (49, 1) = .0, (49, 2) = .0, (49, 3) = .0, (49, 4) = .0, (49, 5) = .0, (49, 6) = .0, (50, 1) = .0, (50, 2) = .0, (50, 3) = .0, (50, 4) = .0, (50, 5) = .0, (50, 6) = .0, (51, 1) = .0, (51, 2) = .0, (51, 3) = .0, (51, 4) = .0, (51, 5) = .0, (51, 6) = .0, (52, 1) = .0, (52, 2) = .0, (52, 3) = .0, (52, 4) = .0, (52, 5) = .0, (52, 6) = .0, (53, 1) = .0, (53, 2) = .0, (53, 3) = .0, (53, 4) = .0, (53, 5) = .0, (53, 6) = .0, (54, 1) = .0, (54, 2) = .0, (54, 3) = .0, (54, 4) = .0, (54, 5) = .0, (54, 6) = .0, (55, 1) = .0, (55, 2) = .0, (55, 3) = .0, (55, 4) = .0, (55, 5) = .0, (55, 6) = .0, (56, 1) = .0, (56, 2) = .0, (56, 3) = .0, (56, 4) = .0, (56, 5) = .0, (56, 6) = .0, (57, 1) = .0, (57, 2) = .0, (57, 3) = .0, (57, 4) = .0, (57, 5) = .0, (57, 6) = .0, (58, 1) = .0, (58, 2) = .0, (58, 3) = .0, (58, 4) = .0, (58, 5) = .0, (58, 6) = .0, (59, 1) = .0, (59, 2) = .0, (59, 3) = .0, (59, 4) = .0, (59, 5) = .0, (59, 6) = .0, (60, 1) = .0, (60, 2) = .0, (60, 3) = .0, (60, 4) = .0, (60, 5) = .0, (60, 6) = .0, (61, 1) = .0, (61, 2) = .0, (61, 3) = .0, (61, 4) = .0, (61, 5) = .0, (61, 6) = .0, (62, 1) = .0, (62, 2) = .0, (62, 3) = .0, (62, 4) = .0, (62, 5) = .0, (62, 6) = .0, (63, 1) = .0, (63, 2) = .0, (63, 3) = .0, (63, 4) = .0, (63, 5) = .0, (63, 6) = .0, (64, 1) = .0, (64, 2) = .0, (64, 3) = .0, (64, 4) = .0, (64, 5) = .0, (64, 6) = .0, (65, 1) = .0, (65, 2) = .0, (65, 3) = .0, (65, 4) = .0, (65, 5) = .0, (65, 6) = .0, (66, 1) = .0, (66, 2) = .0, (66, 3) = .0, (66, 4) = .0, (66, 5) = .0, (66, 6) = .0, (67, 1) = .0, (67, 2) = .0, (67, 3) = .0, (67, 4) = .0, (67, 5) = .0, (67, 6) = .0, (68, 1) = .0, (68, 2) = .0, (68, 3) = .0, (68, 4) = .0, (68, 5) = .0, (68, 6) = .0, (69, 1) = .0, (69, 2) = .0, (69, 3) = .0, (69, 4) = .0, (69, 5) = .0, (69, 6) = .0, (70, 1) = .0, (70, 2) = .0, (70, 3) = .0, (70, 4) = .0, (70, 5) = .0, (70, 6) = .0, (71, 1) = .0, (71, 2) = .0, (71, 3) = .0, (71, 4) = .0, (71, 5) = .0, (71, 6) = .0, (72, 1) = .0, (72, 2) = .0, (72, 3) = .0, (72, 4) = .0, (72, 5) = .0, (72, 6) = .0, (73, 1) = .0, (73, 2) = .0, (73, 3) = .0, (73, 4) = .0, (73, 5) = .0, (73, 6) = .0, (74, 1) = .0, (74, 2) = .0, (74, 3) = .0, (74, 4) = .0, (74, 5) = .0, (74, 6) = .0, (75, 1) = .0, (75, 2) = .0, (75, 3) = .0, (75, 4) = .0, (75, 5) = .0, (75, 6) = .0, (76, 1) = .0, (76, 2) = .0, (76, 3) = .0, (76, 4) = .0, (76, 5) = .0, (76, 6) = .0, (77, 1) = .0, (77, 2) = .0, (77, 3) = .0, (77, 4) = .0, (77, 5) = .0, (77, 6) = .0, (78, 1) = .0, (78, 2) = .0, (78, 3) = .0, (78, 4) = .0, (78, 5) = .0, (78, 6) = .0, (79, 1) = .0, (79, 2) = .0, (79, 3) = .0, (79, 4) = .0, (79, 5) = .0, (79, 6) = .0, (80, 1) = .0, (80, 2) = .0, (80, 3) = .0, (80, 4) = .0, (80, 5) = .0, (80, 6) = .0, (81, 1) = .0, (81, 2) = .0, (81, 3) = .0, (81, 4) = .0, (81, 5) = .0, (81, 6) = .0, (82, 1) = .0, (82, 2) = .0, (82, 3) = .0, (82, 4) = .0, (82, 5) = .0, (82, 6) = .0, (83, 1) = .0, (83, 2) = .0, (83, 3) = .0, (83, 4) = .0, (83, 5) = .0, (83, 6) = .0, (84, 1) = .0, (84, 2) = .0, (84, 3) = .0, (84, 4) = .0, (84, 5) = .0, (84, 6) = .0, (85, 1) = .0, (85, 2) = .0, (85, 3) = .0, (85, 4) = .0, (85, 5) = .0, (85, 6) = .0, (86, 1) = .0, (86, 2) = .0, (86, 3) = .0, (86, 4) = .0, (86, 5) = .0, (86, 6) = .0, (87, 1) = .0, (87, 2) = .0, (87, 3) = .0, (87, 4) = .0, (87, 5) = .0, (87, 6) = .0, (88, 1) = .0, (88, 2) = .0, (88, 3) = .0, (88, 4) = .0, (88, 5) = .0, (88, 6) = .0, (89, 1) = .0, (89, 2) = .0, (89, 3) = .0, (89, 4) = .0, (89, 5) = .0, (89, 6) = .0, (90, 1) = .0, (90, 2) = .0, (90, 3) = .0, (90, 4) = .0, (90, 5) = .0, (90, 6) = .0, (91, 1) = .0, (91, 2) = .0, (91, 3) = .0, (91, 4) = .0, (91, 5) = .0, (91, 6) = .0, (92, 1) = .0, (92, 2) = .0, (92, 3) = .0, (92, 4) = .0, (92, 5) = .0, (92, 6) = .0, (93, 1) = .0, (93, 2) = .0, (93, 3) = .0, (93, 4) = .0, (93, 5) = .0, (93, 6) = .0, (94, 1) = .0, (94, 2) = .0, (94, 3) = .0, (94, 4) = .0, (94, 5) = .0, (94, 6) = .0, (95, 1) = .0, (95, 2) = .0, (95, 3) = .0, (95, 4) = .0, (95, 5) = .0, (95, 6) = .0, (96, 1) = .0, (96, 2) = .0, (96, 3) = .0, (96, 4) = .0, (96, 5) = .0, (96, 6) = .0, (97, 1) = .0, (97, 2) = .0, (97, 3) = .0, (97, 4) = .0, (97, 5) = .0, (97, 6) = .0, (98, 1) = .0, (98, 2) = .0, (98, 3) = .0, (98, 4) = .0, (98, 5) = .0, (98, 6) = .0, (99, 1) = .0, (99, 2) = .0, (99, 3) = .0, (99, 4) = .0, (99, 5) = .0, (99, 6) = .0, (100, 1) = .0, (100, 2) = .0, (100, 3) = .0, (100, 4) = .0, (100, 5) = .0, (100, 6) = .0, (101, 1) = .0, (101, 2) = .0, (101, 3) = .0, (101, 4) = .0, (101, 5) = .0, (101, 6) = .0}, datatype = float[8], order = C_order), ( "solvec1" ) = Vector(101, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0}, datatype = float[8]), ( "allocspace" ) = 101, ( "inputargs" ) = [diff(u(y, t), t) = diff(diff(u(y, t), y), y), {u(0, t) = cos(t), u(10, t) = 0, u(y, 0) = 0}, spacestep = 1/10, timestep = 1/100], ( "periodic" ) = false, ( "startup_only" ) = false, ( "solmat_i2" ) = 0, ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, xi; _s1 := -(1/2)/h^2; _s2 := (h^2+k)/(k*h^2); mat[3] := 1; mat[6*n-3] := 1; for xi from 2 to n-1 do mat[6*xi-3] := _s2; mat[6*xi-4] := _s1; mat[6*xi-2] := _s1 end do end proc, ( "timeadaptive" ) = false, ( "eqndep" ) = [1], ( "explicit" ) = false, ( "depdords" ) = [[[2, 1]]], ( "solvec5" ) = 0, ( "totalwidth" ) = 6, ( "solvec2" ) = Vector(101, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0}, datatype = float[8]), ( "timei" ) = 3, ( "solmat_i1" ) = 0, ( "intspace" ) = Matrix(101, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0, (22, 1) = .0, (23, 1) = .0, (24, 1) = .0, (25, 1) = .0, (26, 1) = .0, (27, 1) = .0, (28, 1) = .0, (29, 1) = .0, (30, 1) = .0, (31, 1) = .0, (32, 1) = .0, (33, 1) = .0, (34, 1) = .0, (35, 1) = .0, (36, 1) = .0, (37, 1) = .0, (38, 1) = .0, (39, 1) = .0, (40, 1) = .0, (41, 1) = .0, (42, 1) = .0, (43, 1) = .0, (44, 1) = .0, (45, 1) = .0, (46, 1) = .0, (47, 1) = .0, (48, 1) = .0, (49, 1) = .0, (50, 1) = .0, (51, 1) = .0, (52, 1) = .0, (53, 1) = .0, (54, 1) = .0, (55, 1) = .0, (56, 1) = .0, (57, 1) = .0, (58, 1) = .0, (59, 1) = .0, (60, 1) = .0, (61, 1) = .0, (62, 1) = .0, (63, 1) = .0, (64, 1) = .0, (65, 1) = .0, (66, 1) = .0, (67, 1) = .0, (68, 1) = .0, (69, 1) = .0, (70, 1) = .0, (71, 1) = .0, (72, 1) = .0, (73, 1) = .0, (74, 1) = .0, (75, 1) = .0, (76, 1) = .0, (77, 1) = .0, (78, 1) = .0, (79, 1) = .0, (80, 1) = .0, (81, 1) = .0, (82, 1) = .0, (83, 1) = .0, (84, 1) = .0, (85, 1) = .0, (86, 1) = .0, (87, 1) = .0, (88, 1) = .0, (89, 1) = .0, (90, 1) = .0, (91, 1) = .0, (92, 1) = .0, (93, 1) = .0, (94, 1) = .0, (95, 1) = .0, (96, 1) = .0, (97, 1) = .0, (98, 1) = .0, (99, 1) = .0, (100, 1) = .0, (101, 1) = .0}, datatype = float[8], order = C_order), ( "fdepvars" ) = [u(y, t)], ( "extrabcs" ) = [0], ( "spaceadaptive" ) = false, ( "autonomous" ) = true, ( "depeqn" ) = [1], ( "solmat_ne" ) = 0, ( "solvec3" ) = Vector(101, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0}, datatype = float[8]), ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "depvars" ) = [u], ( "timevar" ) = t, ( "adjusted" ) = false, ( "leftwidth" ) = 1, ( "stages" ) = 1, ( "errorest" ) = false, ( "BCS", 1 ) = {[[1, 0, 0], b[1, 0, 0]-cos(t)], [[1, 0, 10], b[1, 0, 10]]}, ( "PDEs" ) = [diff(u(y, t), t)-(diff(diff(u(y, t), y), y))], ( "solspace" ) = Vector(101, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = 10.0}, datatype = float[8]), ( "initialized" ) = false ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := [proc (t, x, u) u[1] end proc]; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2:
", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2:
", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "2nd"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc]

This proc captures the value of the solution u:

U := eval(u(y,t), vals);

proc () local tv, xv, solnproc, stype, ndsol, vals; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; Digits := trunc(evalhf(Digits)); solnproc := proc (tv, xv) local INFO, errest, nd, dvars, dary, daryt, daryx, vals, msg, i, j; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; table( [( "soln_procedures" ) = array( 1 .. 1, [( 1 ) = (36893628355780618476)  ] ) ] ) INFO := table( [( "t0" ) = 0, ( "eqnords" ) = [[2, 1]], ( "minspcpoints" ) = 4, ( "norigdepvars" ) = 1, ( "maxords" ) = [2, 1], ( "depshift" ) = [1], ( "solmat_v" ) = Vector(606, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0, (102) = .0, (103) = .0, (104) = .0, (105) = .0, (106) = .0, (107) = .0, (108) = .0, (109) = .0, (110) = .0, (111) = .0, (112) = .0, (113) = .0, (114) = .0, (115) = .0, (116) = .0, (117) = .0, (118) = .0, (119) = .0, (120) = .0, (121) = .0, (122) = .0, (123) = .0, (124) = .0, (125) = .0, (126) = .0, (127) = .0, (128) = .0, (129) = .0, (130) = .0, (131) = .0, (132) = .0, (133) = .0, (134) = .0, (135) = .0, (136) = .0, (137) = .0, (138) = .0, (139) = .0, (140) = .0, (141) = .0, (142) = .0, (143) = .0, (144) = .0, (145) = .0, (146) = .0, (147) = .0, (148) = .0, (149) = .0, (150) = .0, (151) = .0, (152) = .0, (153) = .0, (154) = .0, (155) = .0, (156) = .0, (157) = .0, (158) = .0, (159) = .0, (160) = .0, (161) = .0, (162) = .0, (163) = .0, (164) = .0, (165) = .0, (166) = .0, (167) = .0, (168) = .0, (169) = .0, (170) = .0, (171) = .0, (172) = .0, (173) = .0, (174) = .0, (175) = .0, (176) = .0, (177) = .0, (178) = .0, (179) = .0, (180) = .0, (181) = .0, (182) = .0, (183) = .0, (184) = .0, (185) = .0, (186) = .0, (187) = .0, (188) = .0, (189) = .0, (190) = .0, (191) = .0, (192) = .0, (193) = .0, (194) = .0, (195) = .0, (196) = .0, (197) = .0, (198) = .0, (199) = .0, (200) = .0, (201) = .0, (202) = .0, (203) = .0, (204) = .0, (205) = .0, (206) = .0, (207) = .0, (208) = .0, (209) = .0, (210) = .0, (211) = .0, (212) = .0, (213) = .0, (214) = .0, (215) = .0, (216) = .0, (217) = .0, (218) = .0, (219) = .0, (220) = .0, (221) = .0, (222) = .0, (223) = .0, (224) = .0, (225) = .0, (226) = .0, (227) = .0, (228) = .0, (229) = .0, (230) = .0, (231) = .0, (232) = .0, (233) = .0, (234) = .0, (235) = .0, (236) = .0, (237) = .0, (238) = .0, (239) = .0, (240) = .0, (241) = .0, (242) = .0, (243) = .0, (244) = .0, (245) = .0, (246) = .0, (247) = .0, (248) = .0, (249) = .0, (250) = .0, (251) = .0, (252) = .0, (253) = .0, (254) = .0, (255) = .0, (256) = .0, (257) = .0, (258) = .0, (259) = .0, (260) = .0, (261) = .0, (262) = .0, (263) = .0, (264) = .0, (265) = .0, (266) = .0, (267) = .0, (268) = .0, (269) = .0, (270) = .0, (271) = .0, (272) = .0, (273) = .0, (274) = .0, (275) = .0, (276) = .0, (277) = .0, (278) = .0, (279) = .0, (280) = .0, (281) = .0, (282) = .0, (283) = .0, (284) = .0, (285) = .0, (286) = .0, (287) = .0, (288) = .0, (289) = .0, (290) = .0, (291) = .0, (292) = .0, (293) = .0, (294) = .0, (295) = .0, (296) = .0, (297) = .0, (298) = .0, (299) = .0, (300) = .0, (301) = .0, (302) = .0, (303) = .0, (304) = .0, (305) = .0, (306) = .0, (307) = .0, (308) = .0, (309) = .0, (310) = .0, (311) = .0, (312) = .0, (313) = .0, (314) = .0, (315) = .0, (316) = .0, (317) = .0, (318) = .0, (319) = .0, (320) = .0, (321) = .0, (322) = .0, (323) = .0, (324) = .0, (325) = .0, (326) = .0, (327) = .0, (328) = .0, (329) = .0, (330) = .0, (331) = .0, (332) = .0, (333) = .0, (334) = .0, (335) = .0, (336) = .0, (337) = .0, (338) = .0, (339) = .0, (340) = .0, (341) = .0, (342) = .0, (343) = .0, (344) = .0, (345) = .0, (346) = .0, (347) = .0, (348) = .0, (349) = .0, (350) = .0, (351) = .0, (352) = .0, (353) = .0, (354) = .0, (355) = .0, (356) = .0, (357) = .0, (358) = .0, (359) = .0, (360) = .0, (361) = .0, (362) = .0, (363) = .0, (364) = .0, (365) = .0, (366) = .0, (367) = .0, (368) = .0, (369) = .0, (370) = .0, (371) = .0, (372) = .0, (373) = .0, (374) = .0, (375) = .0, (376) = .0, (377) = .0, (378) = .0, (379) = .0, (380) = .0, (381) = .0, (382) = .0, (383) = .0, (384) = .0, (385) = .0, (386) = .0, (387) = .0, (388) = .0, (389) = .0, (390) = .0, (391) = .0, (392) = .0, (393) = .0, (394) = .0, (395) = .0, (396) = .0, (397) = .0, (398) = .0, (399) = .0, (400) = .0, (401) = .0, (402) = .0, (403) = .0, (404) = .0, (405) = .0, (406) = .0, (407) = .0, (408) = .0, (409) = .0, (410) = .0, (411) = .0, (412) = .0, (413) = .0, (414) = .0, (415) = .0, (416) = .0, (417) = .0, (418) = .0, (419) = .0, (420) = .0, (421) = .0, (422) = .0, (423) = .0, (424) = .0, (425) = .0, (426) = .0, (427) = .0, (428) = .0, (429) = .0, (430) = .0, (431) = .0, (432) = .0, (433) = .0, (434) = .0, (435) = .0, (436) = .0, (437) = .0, (438) = .0, (439) = .0, (440) = .0, (441) = .0, (442) = .0, (443) = .0, (444) = .0, (445) = .0, (446) = .0, (447) = .0, (448) = .0, (449) = .0, (450) = .0, (451) = .0, (452) = .0, (453) = .0, (454) = .0, (455) = .0, (456) = .0, (457) = .0, (458) = .0, (459) = .0, (460) = .0, (461) = .0, (462) = .0, (463) = .0, (464) = .0, (465) = .0, (466) = .0, (467) = .0, (468) = .0, (469) = .0, (470) = .0, (471) = .0, (472) = .0, (473) = .0, (474) = .0, (475) = .0, (476) = .0, (477) = .0, (478) = .0, (479) = .0, (480) = .0, (481) = .0, (482) = .0, (483) = .0, (484) = .0, (485) = .0, (486) = .0, (487) = .0, (488) = .0, (489) = .0, (490) = .0, (491) = .0, (492) = .0, (493) = .0, (494) = .0, (495) = .0, (496) = .0, (497) = .0, (498) = .0, (499) = .0, (500) = .0, (501) = .0, (502) = .0, (503) = .0, (504) = .0, (505) = .0, (506) = .0, (507) = .0, (508) = .0, (509) = .0, (510) = .0, (511) = .0, (512) = .0, (513) = .0, (514) = .0, (515) = .0, (516) = .0, (517) = .0, (518) = .0, (519) = .0, (520) = .0, (521) = .0, (522) = .0, (523) = .0, (524) = .0, (525) = .0, (526) = .0, (527) = .0, (528) = .0, (529) = .0, (530) = .0, (531) = .0, (532) = .0, (533) = .0, (534) = .0, (535) = .0, (536) = .0, (537) = .0, (538) = .0, (539) = .0, (540) = .0, (541) = .0, (542) = .0, (543) = .0, (544) = .0, (545) = .0, (546) = .0, (547) = .0, (548) = .0, (549) = .0, (550) = .0, (551) = .0, (552) = .0, (553) = .0, (554) = .0, (555) = .0, (556) = .0, (557) = .0, (558) = .0, (559) = .0, (560) = .0, (561) = .0, (562) = .0, (563) = .0, (564) = .0, (565) = .0, (566) = .0, (567) = .0, (568) = .0, (569) = .0, (570) = .0, (571) = .0, (572) = .0, (573) = .0, (574) = .0, (575) = .0, (576) = .0, (577) = .0, (578) = .0, (579) = .0, (580) = .0, (581) = .0, (582) = .0, (583) = .0, (584) = .0, (585) = .0, (586) = .0, (587) = .0, (588) = .0, (589) = .0, (590) = .0, (591) = .0, (592) = .0, (593) = .0, (594) = .0, (595) = .0, (596) = .0, (597) = .0, (598) = .0, (599) = .0, (600) = .0, (601) = .0, (602) = .0, (603) = .0, (604) = .0, (605) = .0, (606) = .0}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(101, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (42, 1) = .0, (42, 2) = .0, (42, 3) = .0, (42, 4) = .0, (42, 5) = .0, (42, 6) = .0, (43, 1) = .0, (43, 2) = .0, (43, 3) = .0, (43, 4) = .0, (43, 5) = .0, (43, 6) = .0, (44, 1) = .0, (44, 2) = .0, (44, 3) = .0, (44, 4) = .0, (44, 5) = .0, (44, 6) = .0, (45, 1) = .0, (45, 2) = .0, (45, 3) = .0, (45, 4) = .0, (45, 5) = .0, (45, 6) = .0, (46, 1) = .0, (46, 2) = .0, (46, 3) = .0, (46, 4) = .0, (46, 5) = .0, (46, 6) = .0, (47, 1) = .0, (47, 2) = .0, (47, 3) = .0, (47, 4) = .0, (47, 5) = .0, (47, 6) = .0, (48, 1) = .0, (48, 2) = .0, (48, 3) = .0, (48, 4) = .0, (48, 5) = .0, (48, 6) = .0, (49, 1) = .0, (49, 2) = .0, (49, 3) = .0, (49, 4) = .0, (49, 5) = .0, (49, 6) = .0, (50, 1) = .0, (50, 2) = .0, (50, 3) = .0, (50, 4) = .0, (50, 5) = .0, (50, 6) = .0, (51, 1) = .0, (51, 2) = .0, (51, 3) = .0, (51, 4) = .0, (51, 5) = .0, (51, 6) = .0, (52, 1) = .0, (52, 2) = .0, (52, 3) = .0, (52, 4) = .0, (52, 5) = .0, (52, 6) = .0, (53, 1) = .0, (53, 2) = .0, (53, 3) = .0, (53, 4) = .0, (53, 5) = .0, (53, 6) = .0, (54, 1) = .0, (54, 2) = .0, (54, 3) = .0, (54, 4) = .0, (54, 5) = .0, (54, 6) = .0, (55, 1) = .0, (55, 2) = .0, (55, 3) = .0, (55, 4) = .0, (55, 5) = .0, (55, 6) = .0, (56, 1) = .0, (56, 2) = .0, (56, 3) = .0, (56, 4) = .0, (56, 5) = .0, (56, 6) = .0, (57, 1) = .0, (57, 2) = .0, (57, 3) = .0, (57, 4) = .0, (57, 5) = .0, (57, 6) = .0, (58, 1) = .0, (58, 2) = .0, (58, 3) = .0, (58, 4) = .0, (58, 5) = .0, (58, 6) = .0, (59, 1) = .0, (59, 2) = .0, (59, 3) = .0, (59, 4) = .0, (59, 5) = .0, (59, 6) = .0, (60, 1) = .0, (60, 2) = .0, (60, 3) = .0, (60, 4) = .0, (60, 5) = .0, (60, 6) = .0, (61, 1) = .0, (61, 2) = .0, (61, 3) = .0, (61, 4) = .0, (61, 5) = .0, (61, 6) = .0, (62, 1) = .0, (62, 2) = .0, (62, 3) = .0, (62, 4) = .0, (62, 5) = .0, (62, 6) = .0, (63, 1) = .0, (63, 2) = .0, (63, 3) = .0, (63, 4) = .0, (63, 5) = .0, (63, 6) = .0, (64, 1) = .0, (64, 2) = .0, (64, 3) = .0, (64, 4) = .0, (64, 5) = .0, (64, 6) = .0, (65, 1) = .0, (65, 2) = .0, (65, 3) = .0, (65, 4) = .0, (65, 5) = .0, (65, 6) = .0, (66, 1) = .0, (66, 2) = .0, (66, 3) = .0, (66, 4) = .0, (66, 5) = .0, (66, 6) = .0, (67, 1) = .0, (67, 2) = .0, (67, 3) = .0, (67, 4) = .0, (67, 5) = .0, (67, 6) = .0, (68, 1) = .0, (68, 2) = .0, (68, 3) = .0, (68, 4) = .0, (68, 5) = .0, (68, 6) = .0, (69, 1) = .0, (69, 2) = .0, (69, 3) = .0, (69, 4) = .0, (69, 5) = .0, (69, 6) = .0, (70, 1) = .0, (70, 2) = .0, (70, 3) = .0, (70, 4) = .0, (70, 5) = .0, (70, 6) = .0, (71, 1) = .0, (71, 2) = .0, (71, 3) = .0, (71, 4) = .0, (71, 5) = .0, (71, 6) = .0, (72, 1) = .0, (72, 2) = .0, (72, 3) = .0, (72, 4) = .0, (72, 5) = .0, (72, 6) = .0, (73, 1) = .0, (73, 2) = .0, (73, 3) = .0, (73, 4) = .0, (73, 5) = .0, (73, 6) = .0, (74, 1) = .0, (74, 2) = .0, (74, 3) = .0, (74, 4) = .0, (74, 5) = .0, (74, 6) = .0, (75, 1) = .0, (75, 2) = .0, (75, 3) = .0, (75, 4) = .0, (75, 5) = .0, (75, 6) = .0, (76, 1) = .0, (76, 2) = .0, (76, 3) = .0, (76, 4) = .0, (76, 5) = .0, (76, 6) = .0, (77, 1) = .0, (77, 2) = .0, (77, 3) = .0, (77, 4) = .0, (77, 5) = .0, (77, 6) = .0, (78, 1) = .0, (78, 2) = .0, (78, 3) = .0, (78, 4) = .0, (78, 5) = .0, (78, 6) = .0, (79, 1) = .0, (79, 2) = .0, (79, 3) = .0, (79, 4) = .0, (79, 5) = .0, (79, 6) = .0, (80, 1) = .0, (80, 2) = .0, (80, 3) = .0, (80, 4) = .0, (80, 5) = .0, (80, 6) = .0, (81, 1) = .0, (81, 2) = .0, (81, 3) = .0, (81, 4) = .0, (81, 5) = .0, (81, 6) = .0, (82, 1) = .0, (82, 2) = .0, (82, 3) = .0, (82, 4) = .0, (82, 5) = .0, (82, 6) = .0, (83, 1) = .0, (83, 2) = .0, (83, 3) = .0, (83, 4) = .0, (83, 5) = .0, (83, 6) = .0, (84, 1) = .0, (84, 2) = .0, (84, 3) = .0, (84, 4) = .0, (84, 5) = .0, (84, 6) = .0, (85, 1) = .0, (85, 2) = .0, (85, 3) = .0, (85, 4) = .0, (85, 5) = .0, (85, 6) = .0, (86, 1) = .0, (86, 2) = .0, (86, 3) = .0, (86, 4) = .0, (86, 5) = .0, (86, 6) = .0, (87, 1) = .0, (87, 2) = .0, (87, 3) = .0, (87, 4) = .0, (87, 5) = .0, (87, 6) = .0, (88, 1) = .0, (88, 2) = .0, (88, 3) = .0, (88, 4) = .0, (88, 5) = .0, (88, 6) = .0, (89, 1) = .0, (89, 2) = .0, (89, 3) = .0, (89, 4) = .0, (89, 5) = .0, (89, 6) = .0, (90, 1) = .0, (90, 2) = .0, (90, 3) = .0, (90, 4) = .0, (90, 5) = .0, (90, 6) = .0, (91, 1) = .0, (91, 2) = .0, (91, 3) = .0, (91, 4) = .0, (91, 5) = .0, (91, 6) = .0, (92, 1) = .0, (92, 2) = .0, (92, 3) = .0, (92, 4) = .0, (92, 5) = .0, (92, 6) = .0, (93, 1) = .0, (93, 2) = .0, (93, 3) = .0, (93, 4) = .0, (93, 5) = .0, (93, 6) = .0, (94, 1) = .0, (94, 2) = .0, (94, 3) = .0, (94, 4) = .0, (94, 5) = .0, (94, 6) = .0, (95, 1) = .0, (95, 2) = .0, (95, 3) = .0, (95, 4) = .0, (95, 5) = .0, (95, 6) = .0, (96, 1) = .0, (96, 2) = .0, (96, 3) = .0, (96, 4) = .0, (96, 5) = .0, (96, 6) = .0, (97, 1) = .0, (97, 2) = .0, (97, 3) = .0, (97, 4) = .0, (97, 5) = .0, (97, 6) = .0, (98, 1) = .0, (98, 2) = .0, (98, 3) = .0, (98, 4) = .0, (98, 5) = .0, (98, 6) = .0, (99, 1) = .0, (99, 2) = .0, (99, 3) = .0, (99, 4) = .0, (99, 5) = .0, (99, 6) = .0, (100, 1) = .0, (100, 2) = .0, (100, 3) = .0, (100, 4) = .0, (100, 5) = .0, (100, 6) = .0, (101, 1) = .0, (101, 2) = .0, (101, 3) = .0, (101, 4) = .0, (101, 5) = .0, (101, 6) = .0}, datatype = float[8], order = C_order))]), ( "spacevar" ) = y, ( "timeidx" ) = 2, ( "depords" ) = [[2, 1]], ( "theta" ) = 1/2, ( "erroraccum" ) = true, ( "spacepts" ) = 101, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, xi; _s2 := 1/k; _s3 := (1/2)/h^2; vec[1] := cos(t+k); vec[n] := 0; for xi from 2 to n-1 do _s1 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := _s3*_s1+_s2*vp[xi] end do end proc, ( "rightwidth" ) = 0, ( "ICS" ) = [0], ( "matrixhf" ) = true, ( "IBC" ) = b, ( "bandwidth" ) = [1, 2], ( "pts", y ) = [0, 10], ( "dependson" ) = [{1}], ( "vectorhf" ) = true, ( "spaceidx" ) = 1, ( "banded" ) = true, ( "solvec4" ) = 0, ( "indepvars" ) = [y, t], ( "spacestep" ) = .100000000000000, ( "linear" ) = true, ( "timestep" ) = 0.100000000000000e-1, ( "mixed" ) = false, ( "method" ) = theta, ( "solmat_is" ) = 0, ( "solution" ) = Array(1..3, 1..101, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (1, 22, 1) = .0, (1, 23, 1) = .0, (1, 24, 1) = .0, (1, 25, 1) = .0, (1, 26, 1) = .0, (1, 27, 1) = .0, (1, 28, 1) = .0, (1, 29, 1) = .0, (1, 30, 1) = .0, (1, 31, 1) = .0, (1, 32, 1) = .0, (1, 33, 1) = .0, (1, 34, 1) = .0, (1, 35, 1) = .0, (1, 36, 1) = .0, (1, 37, 1) = .0, (1, 38, 1) = .0, (1, 39, 1) = .0, (1, 40, 1) = .0, (1, 41, 1) = .0, (1, 42, 1) = .0, (1, 43, 1) = .0, (1, 44, 1) = .0, (1, 45, 1) = .0, (1, 46, 1) = .0, (1, 47, 1) = .0, (1, 48, 1) = .0, (1, 49, 1) = .0, (1, 50, 1) = .0, (1, 51, 1) = .0, (1, 52, 1) = .0, (1, 53, 1) = .0, (1, 54, 1) = .0, (1, 55, 1) = .0, (1, 56, 1) = .0, (1, 57, 1) = .0, (1, 58, 1) = .0, (1, 59, 1) = .0, (1, 60, 1) = .0, (1, 61, 1) = .0, (1, 62, 1) = .0, (1, 63, 1) = .0, (1, 64, 1) = .0, (1, 65, 1) = .0, (1, 66, 1) = .0, (1, 67, 1) = .0, (1, 68, 1) = .0, (1, 69, 1) = .0, (1, 70, 1) = .0, (1, 71, 1) = .0, (1, 72, 1) = .0, (1, 73, 1) = .0, (1, 74, 1) = .0, (1, 75, 1) = .0, (1, 76, 1) = .0, (1, 77, 1) = .0, (1, 78, 1) = .0, (1, 79, 1) = .0, (1, 80, 1) = .0, (1, 81, 1) = .0, (1, 82, 1) = .0, (1, 83, 1) = .0, (1, 84, 1) = .0, (1, 85, 1) = .0, (1, 86, 1) = .0, (1, 87, 1) = .0, (1, 88, 1) = .0, (1, 89, 1) = .0, (1, 90, 1) = .0, (1, 91, 1) = .0, (1, 92, 1) = .0, (1, 93, 1) = .0, (1, 94, 1) = .0, (1, 95, 1) = .0, (1, 96, 1) = .0, (1, 97, 1) = .0, (1, 98, 1) = .0, (1, 99, 1) = .0, (1, 100, 1) = .0, (1, 101, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (2, 22, 1) = .0, (2, 23, 1) = .0, (2, 24, 1) = .0, (2, 25, 1) = .0, (2, 26, 1) = .0, (2, 27, 1) = .0, (2, 28, 1) = .0, (2, 29, 1) = .0, (2, 30, 1) = .0, (2, 31, 1) = .0, (2, 32, 1) = .0, (2, 33, 1) = .0, (2, 34, 1) = .0, (2, 35, 1) = .0, (2, 36, 1) = .0, (2, 37, 1) = .0, (2, 38, 1) = .0, (2, 39, 1) = .0, (2, 40, 1) = .0, (2, 41, 1) = .0, (2, 42, 1) = .0, (2, 43, 1) = .0, (2, 44, 1) = .0, (2, 45, 1) = .0, (2, 46, 1) = .0, (2, 47, 1) = .0, (2, 48, 1) = .0, (2, 49, 1) = .0, (2, 50, 1) = .0, (2, 51, 1) = .0, (2, 52, 1) = .0, (2, 53, 1) = .0, (2, 54, 1) = .0, (2, 55, 1) = .0, (2, 56, 1) = .0, (2, 57, 1) = .0, (2, 58, 1) = .0, (2, 59, 1) = .0, (2, 60, 1) = .0, (2, 61, 1) = .0, (2, 62, 1) = .0, (2, 63, 1) = .0, (2, 64, 1) = .0, (2, 65, 1) = .0, (2, 66, 1) = .0, (2, 67, 1) = .0, (2, 68, 1) = .0, (2, 69, 1) = .0, (2, 70, 1) = .0, (2, 71, 1) = .0, (2, 72, 1) = .0, (2, 73, 1) = .0, (2, 74, 1) = .0, (2, 75, 1) = .0, (2, 76, 1) = .0, (2, 77, 1) = .0, (2, 78, 1) = .0, (2, 79, 1) = .0, (2, 80, 1) = .0, (2, 81, 1) = .0, (2, 82, 1) = .0, (2, 83, 1) = .0, (2, 84, 1) = .0, (2, 85, 1) = .0, (2, 86, 1) = .0, (2, 87, 1) = .0, (2, 88, 1) = .0, (2, 89, 1) = .0, (2, 90, 1) = .0, (2, 91, 1) = .0, (2, 92, 1) = .0, (2, 93, 1) = .0, (2, 94, 1) = .0, (2, 95, 1) = .0, (2, 96, 1) = .0, (2, 97, 1) = .0, (2, 98, 1) = .0, (2, 99, 1) = .0, (2, 100, 1) = .0, (2, 101, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0, (3, 22, 1) = .0, (3, 23, 1) = .0, (3, 24, 1) = .0, (3, 25, 1) = .0, (3, 26, 1) = .0, (3, 27, 1) = .0, (3, 28, 1) = .0, (3, 29, 1) = .0, (3, 30, 1) = .0, (3, 31, 1) = .0, (3, 32, 1) = .0, (3, 33, 1) = .0, (3, 34, 1) = .0, (3, 35, 1) = .0, (3, 36, 1) = .0, (3, 37, 1) = .0, (3, 38, 1) = .0, (3, 39, 1) = .0, (3, 40, 1) = .0, (3, 41, 1) = .0, (3, 42, 1) = .0, (3, 43, 1) = .0, (3, 44, 1) = .0, (3, 45, 1) = .0, (3, 46, 1) = .0, (3, 47, 1) = .0, (3, 48, 1) = .0, (3, 49, 1) = .0, (3, 50, 1) = .0, (3, 51, 1) = .0, (3, 52, 1) = .0, (3, 53, 1) = .0, (3, 54, 1) = .0, (3, 55, 1) = .0, (3, 56, 1) = .0, (3, 57, 1) = .0, (3, 58, 1) = .0, (3, 59, 1) = .0, (3, 60, 1) = .0, (3, 61, 1) = .0, (3, 62, 1) = .0, (3, 63, 1) = .0, (3, 64, 1) = .0, (3, 65, 1) = .0, (3, 66, 1) = .0, (3, 67, 1) = .0, (3, 68, 1) = .0, (3, 69, 1) = .0, (3, 70, 1) = .0, (3, 71, 1) = .0, (3, 72, 1) = .0, (3, 73, 1) = .0, (3, 74, 1) = .0, (3, 75, 1) = .0, (3, 76, 1) = .0, (3, 77, 1) = .0, (3, 78, 1) = .0, (3, 79, 1) = .0, (3, 80, 1) = .0, (3, 81, 1) = .0, (3, 82, 1) = .0, (3, 83, 1) = .0, (3, 84, 1) = .0, (3, 85, 1) = .0, (3, 86, 1) = .0, (3, 87, 1) = .0, (3, 88, 1) = .0, (3, 89, 1) = .0, (3, 90, 1) = .0, (3, 91, 1) = .0, (3, 92, 1) = .0, (3, 93, 1) = .0, (3, 94, 1) = .0, (3, 95, 1) = .0, (3, 96, 1) = .0, (3, 97, 1) = .0, (3, 98, 1) = .0, (3, 99, 1) = .0, (3, 100, 1) = .0, (3, 101, 1) = .0}, datatype = float[8], order = C_order), ( "multidep" ) = [false, false], ( "solmatrix" ) = Matrix(101, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (42, 1) = .0, (42, 2) = .0, (42, 3) = .0, (42, 4) = .0, (42, 5) = .0, (42, 6) = .0, (43, 1) = .0, (43, 2) = .0, (43, 3) = .0, (43, 4) = .0, (43, 5) = .0, (43, 6) = .0, (44, 1) = .0, (44, 2) = .0, (44, 3) = .0, (44, 4) = .0, (44, 5) = .0, (44, 6) = .0, (45, 1) = .0, (45, 2) = .0, (45, 3) = .0, (45, 4) = .0, (45, 5) = .0, (45, 6) = .0, (46, 1) = .0, (46, 2) = .0, (46, 3) = .0, (46, 4) = .0, (46, 5) = .0, (46, 6) = .0, (47, 1) = .0, (47, 2) = .0, (47, 3) = .0, (47, 4) = .0, (47, 5) = .0, (47, 6) = .0, (48, 1) = .0, (48, 2) = .0, (48, 3) = .0, (48, 4) = .0, (48, 5) = .0, (48, 6) = .0, (49, 1) = .0, (49, 2) = .0, (49, 3) = .0, (49, 4) = .0, (49, 5) = .0, (49, 6) = .0, (50, 1) = .0, (50, 2) = .0, (50, 3) = .0, (50, 4) = .0, (50, 5) = .0, (50, 6) = .0, (51, 1) = .0, (51, 2) = .0, (51, 3) = .0, (51, 4) = .0, (51, 5) = .0, (51, 6) = .0, (52, 1) = .0, (52, 2) = .0, (52, 3) = .0, (52, 4) = .0, (52, 5) = .0, (52, 6) = .0, (53, 1) = .0, (53, 2) = .0, (53, 3) = .0, (53, 4) = .0, (53, 5) = .0, (53, 6) = .0, (54, 1) = .0, (54, 2) = .0, (54, 3) = .0, (54, 4) = .0, (54, 5) = .0, (54, 6) = .0, (55, 1) = .0, (55, 2) = .0, (55, 3) = .0, (55, 4) = .0, (55, 5) = .0, (55, 6) = .0, (56, 1) = .0, (56, 2) = .0, (56, 3) = .0, (56, 4) = .0, (56, 5) = .0, (56, 6) = .0, (57, 1) = .0, (57, 2) = .0, (57, 3) = .0, (57, 4) = .0, (57, 5) = .0, (57, 6) = .0, (58, 1) = .0, (58, 2) = .0, (58, 3) = .0, (58, 4) = .0, (58, 5) = .0, (58, 6) = .0, (59, 1) = .0, (59, 2) = .0, (59, 3) = .0, (59, 4) = .0, (59, 5) = .0, (59, 6) = .0, (60, 1) = .0, (60, 2) = .0, (60, 3) = .0, (60, 4) = .0, (60, 5) = .0, (60, 6) = .0, (61, 1) = .0, (61, 2) = .0, (61, 3) = .0, (61, 4) = .0, (61, 5) = .0, (61, 6) = .0, (62, 1) = .0, (62, 2) = .0, (62, 3) = .0, (62, 4) = .0, (62, 5) = .0, (62, 6) = .0, (63, 1) = .0, (63, 2) = .0, (63, 3) = .0, (63, 4) = .0, (63, 5) = .0, (63, 6) = .0, (64, 1) = .0, (64, 2) = .0, (64, 3) = .0, (64, 4) = .0, (64, 5) = .0, (64, 6) = .0, (65, 1) = .0, (65, 2) = .0, (65, 3) = .0, (65, 4) = .0, (65, 5) = .0, (65, 6) = .0, (66, 1) = .0, (66, 2) = .0, (66, 3) = .0, (66, 4) = .0, (66, 5) = .0, (66, 6) = .0, (67, 1) = .0, (67, 2) = .0, (67, 3) = .0, (67, 4) = .0, (67, 5) = .0, (67, 6) = .0, (68, 1) = .0, (68, 2) = .0, (68, 3) = .0, (68, 4) = .0, (68, 5) = .0, (68, 6) = .0, (69, 1) = .0, (69, 2) = .0, (69, 3) = .0, (69, 4) = .0, (69, 5) = .0, (69, 6) = .0, (70, 1) = .0, (70, 2) = .0, (70, 3) = .0, (70, 4) = .0, (70, 5) = .0, (70, 6) = .0, (71, 1) = .0, (71, 2) = .0, (71, 3) = .0, (71, 4) = .0, (71, 5) = .0, (71, 6) = .0, (72, 1) = .0, (72, 2) = .0, (72, 3) = .0, (72, 4) = .0, (72, 5) = .0, (72, 6) = .0, (73, 1) = .0, (73, 2) = .0, (73, 3) = .0, (73, 4) = .0, (73, 5) = .0, (73, 6) = .0, (74, 1) = .0, (74, 2) = .0, (74, 3) = .0, (74, 4) = .0, (74, 5) = .0, (74, 6) = .0, (75, 1) = .0, (75, 2) = .0, (75, 3) = .0, (75, 4) = .0, (75, 5) = .0, (75, 6) = .0, (76, 1) = .0, (76, 2) = .0, (76, 3) = .0, (76, 4) = .0, (76, 5) = .0, (76, 6) = .0, (77, 1) = .0, (77, 2) = .0, (77, 3) = .0, (77, 4) = .0, (77, 5) = .0, (77, 6) = .0, (78, 1) = .0, (78, 2) = .0, (78, 3) = .0, (78, 4) = .0, (78, 5) = .0, (78, 6) = .0, (79, 1) = .0, (79, 2) = .0, (79, 3) = .0, (79, 4) = .0, (79, 5) = .0, (79, 6) = .0, (80, 1) = .0, (80, 2) = .0, (80, 3) = .0, (80, 4) = .0, (80, 5) = .0, (80, 6) = .0, (81, 1) = .0, (81, 2) = .0, (81, 3) = .0, (81, 4) = .0, (81, 5) = .0, (81, 6) = .0, (82, 1) = .0, (82, 2) = .0, (82, 3) = .0, (82, 4) = .0, (82, 5) = .0, (82, 6) = .0, (83, 1) = .0, (83, 2) = .0, (83, 3) = .0, (83, 4) = .0, (83, 5) = .0, (83, 6) = .0, (84, 1) = .0, (84, 2) = .0, (84, 3) = .0, (84, 4) = .0, (84, 5) = .0, (84, 6) = .0, (85, 1) = .0, (85, 2) = .0, (85, 3) = .0, (85, 4) = .0, (85, 5) = .0, (85, 6) = .0, (86, 1) = .0, (86, 2) = .0, (86, 3) = .0, (86, 4) = .0, (86, 5) = .0, (86, 6) = .0, (87, 1) = .0, (87, 2) = .0, (87, 3) = .0, (87, 4) = .0, (87, 5) = .0, (87, 6) = .0, (88, 1) = .0, (88, 2) = .0, (88, 3) = .0, (88, 4) = .0, (88, 5) = .0, (88, 6) = .0, (89, 1) = .0, (89, 2) = .0, (89, 3) = .0, (89, 4) = .0, (89, 5) = .0, (89, 6) = .0, (90, 1) = .0, (90, 2) = .0, (90, 3) = .0, (90, 4) = .0, (90, 5) = .0, (90, 6) = .0, (91, 1) = .0, (91, 2) = .0, (91, 3) = .0, (91, 4) = .0, (91, 5) = .0, (91, 6) = .0, (92, 1) = .0, (92, 2) = .0, (92, 3) = .0, (92, 4) = .0, (92, 5) = .0, (92, 6) = .0, (93, 1) = .0, (93, 2) = .0, (93, 3) = .0, (93, 4) = .0, (93, 5) = .0, (93, 6) = .0, (94, 1) = .0, (94, 2) = .0, (94, 3) = .0, (94, 4) = .0, (94, 5) = .0, (94, 6) = .0, (95, 1) = .0, (95, 2) = .0, (95, 3) = .0, (95, 4) = .0, (95, 5) = .0, (95, 6) = .0, (96, 1) = .0, (96, 2) = .0, (96, 3) = .0, (96, 4) = .0, (96, 5) = .0, (96, 6) = .0, (97, 1) = .0, (97, 2) = .0, (97, 3) = .0, (97, 4) = .0, (97, 5) = .0, (97, 6) = .0, (98, 1) = .0, (98, 2) = .0, (98, 3) = .0, (98, 4) = .0, (98, 5) = .0, (98, 6) = .0, (99, 1) = .0, (99, 2) = .0, (99, 3) = .0, (99, 4) = .0, (99, 5) = .0, (99, 6) = .0, (100, 1) = .0, (100, 2) = .0, (100, 3) = .0, (100, 4) = .0, (100, 5) = .0, (100, 6) = .0, (101, 1) = .0, (101, 2) = .0, (101, 3) = .0, (101, 4) = .0, (101, 5) = .0, (101, 6) = .0}, datatype = float[8], order = C_order), ( "solvec1" ) = Vector(101, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0}, datatype = float[8]), ( "allocspace" ) = 101, ( "inputargs" ) = [diff(u(y, t), t) = diff(diff(u(y, t), y), y), {u(0, t) = cos(t), u(10, t) = 0, u(y, 0) = 0}, spacestep = 1/10, timestep = 1/100], ( "periodic" ) = false, ( "startup_only" ) = false, ( "solmat_i2" ) = 0, ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, xi; _s1 := -(1/2)/h^2; _s2 := (h^2+k)/(k*h^2); mat[3] := 1; mat[6*n-3] := 1; for xi from 2 to n-1 do mat[6*xi-3] := _s2; mat[6*xi-4] := _s1; mat[6*xi-2] := _s1 end do end proc, ( "timeadaptive" ) = false, ( "eqndep" ) = [1], ( "explicit" ) = false, ( "depdords" ) = [[[2, 1]]], ( "solvec5" ) = 0, ( "totalwidth" ) = 6, ( "solvec2" ) = Vector(101, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0}, datatype = float[8]), ( "timei" ) = 3, ( "solmat_i1" ) = 0, ( "intspace" ) = Matrix(101, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0, (22, 1) = .0, (23, 1) = .0, (24, 1) = .0, (25, 1) = .0, (26, 1) = .0, (27, 1) = .0, (28, 1) = .0, (29, 1) = .0, (30, 1) = .0, (31, 1) = .0, (32, 1) = .0, (33, 1) = .0, (34, 1) = .0, (35, 1) = .0, (36, 1) = .0, (37, 1) = .0, (38, 1) = .0, (39, 1) = .0, (40, 1) = .0, (41, 1) = .0, (42, 1) = .0, (43, 1) = .0, (44, 1) = .0, (45, 1) = .0, (46, 1) = .0, (47, 1) = .0, (48, 1) = .0, (49, 1) = .0, (50, 1) = .0, (51, 1) = .0, (52, 1) = .0, (53, 1) = .0, (54, 1) = .0, (55, 1) = .0, (56, 1) = .0, (57, 1) = .0, (58, 1) = .0, (59, 1) = .0, (60, 1) = .0, (61, 1) = .0, (62, 1) = .0, (63, 1) = .0, (64, 1) = .0, (65, 1) = .0, (66, 1) = .0, (67, 1) = .0, (68, 1) = .0, (69, 1) = .0, (70, 1) = .0, (71, 1) = .0, (72, 1) = .0, (73, 1) = .0, (74, 1) = .0, (75, 1) = .0, (76, 1) = .0, (77, 1) = .0, (78, 1) = .0, (79, 1) = .0, (80, 1) = .0, (81, 1) = .0, (82, 1) = .0, (83, 1) = .0, (84, 1) = .0, (85, 1) = .0, (86, 1) = .0, (87, 1) = .0, (88, 1) = .0, (89, 1) = .0, (90, 1) = .0, (91, 1) = .0, (92, 1) = .0, (93, 1) = .0, (94, 1) = .0, (95, 1) = .0, (96, 1) = .0, (97, 1) = .0, (98, 1) = .0, (99, 1) = .0, (100, 1) = .0, (101, 1) = .0}, datatype = float[8], order = C_order), ( "fdepvars" ) = [u(y, t)], ( "extrabcs" ) = [0], ( "spaceadaptive" ) = false, ( "autonomous" ) = true, ( "depeqn" ) = [1], ( "solmat_ne" ) = 0, ( "solvec3" ) = Vector(101, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0}, datatype = float[8]), ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "depvars" ) = [u], ( "timevar" ) = t, ( "adjusted" ) = false, ( "leftwidth" ) = 1, ( "stages" ) = 1, ( "errorest" ) = false, ( "BCS", 1 ) = {[[1, 0, 0], b[1, 0, 0]-cos(t)], [[1, 0, 10], b[1, 0, 10]]}, ( "PDEs" ) = [diff(u(y, t), t)-(diff(diff(u(y, t), y), y))], ( "solspace" ) = Vector(101, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = 10.0}, datatype = float[8]), ( "initialized" ) = false ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := [proc (t, x, u) u[1] end proc]; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2:
", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2:
", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "2nd"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc

Here is the solution evaluated at 0, .1:

U(0,0.1);

.995004165278025710

Here is the flux, "-(&PartialD; u)/(&PartialD; y)", evaluated at 1, .5:

-D[1](U)(1,0.5);

.4534226475

That evaluation fails at the boundary, I don't know why:

-D[1](U)(0,0.5);

-(D[1](U))(0, .5)

But we can work around that.  We approximate the y derivative at y = 0 through
the finite difference (U(`&epsilon;`, t)-U(0, t))/`&epsilon;` for a small value of `&epsilon;`.  Experiemnts

show that `&epsilon;` = 10^(-2) provides a good enough accuracy.  Reducing to `&epsilon;` = 10^(-3) 

make no noticeable change.

eps := 1e-3;

0.1e-2

boundary_flux := t -> -(U(eps,t) - U(0,t))/eps;

proc (t) options operator, arrow; -(U(eps, t)-U(0, t))/eps end proc

plot(boundary_flux(t), t=0..Pi);

Note: The boundary flux goes to infinity as proc (t) options operator, arrow; LinearAlgebra:-Transpose(0) end proc.  That's due to the discontinuity

which has been discussed earlier.

 

@wmcnally I see that in the case of the pendulum equations you have

sys := A:-Linearize(format=all)

while in the case of the RLC circuit you also specify params and paramcheck.  Perhaps that's the reason for the pendulum case not working?  That's just an observation; I know nothing about Maplesim.

If you don't receive further suggestions to your question here, you may want to ask for help by emailing <support@maplesoft.com>.

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