Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Using insert sequences: `%*`(seq(...))

 

Behaves very poorly when the sequence has one element. E.g., if this is a double sequence(say a double sum) then when the inner seq/sum has one element the inert visual is poorly displayed with extra junk rather than just showing one element.

`%+`(floor(5 %/ (2 %* 3 %* 5)))

 

E.g., rathernt han just showing:

(floor(5 %/ (2 %* 3 %* 5)))

 

Is there any way to get it to play nice without having to modify the functions/(this is a global problem so it deserves a global solution rather than ad-hoc that has to be applied to every usage).

 

 

I have some algebraic expression which I want to expand.

I used the ExpandSteps command to show me the steps, but I guess I used it incorrectly.

Attached below the file with the commands.

It should be expanded to -\Delta*\sin^2(\theta), but I want maple to show me the steps.

ExpandSteps.mw
 

"with(Student[Basics]):  Delta:=r^(2)-2 M*r+a^(2);  rho^():=sqrt(r^(2)+a^(2)*(cos(theta))^(2));  ExpandSteps((a^(2)*sin^(2)(theta)-Delta^(2))*((r^(2)+a^(2))^(2)-a^(2 )*Delta*sin^(2)(theta))*((sin^(2)(theta))/(rho^(4)))-(4 *a^(2)*M^(2)*r^(2)*sin^(4)(theta))/(rho^(4)))"

Error, (in Student:-Basics:-ExpandSteps) too many levels of recursion

 

NULL


 

Download ExpandSteps.mw

 

Let A(-2,3,-5),B(-6,1,-1),C(2,-3,7) and point D on BC where the angle  DAB = angle DAC  .Find the equation of line AD?

Hello everyone,

While trying to open a maple document, a box pops up with the text "How do you want to open this file?" with the options "Maple Text, Plain Text, Maple Inputs" what could be responsible for this? and which of the options is better for mathematics and coding?

 

Thank you so much

Dear maple users,

A fine day wishes to all.

I have solved the PDE via PDsolve. Here I need to calculate the Psi function. How to calculate the indefinite integral and how to find the constant-coefficient (C1).

Here Psi=0 at x=0

int_c.mw


 

restart:

with(PDEtools):

with(plots):

fcns := {f(x,t),theta(x,t)};

{f(x, t), theta(x, t)}

(1)

d:=0.5:xi:=0.1:

R:=z->piecewise(d<=z and z<=d+1,1-2*xi*(cos((2*3.14)*((z-d)*(1/2))-1/4)-(7/100)*cos((32*3.14)*(z-d-1/2))),1);

proc (z) options operator, arrow; piecewise(d <= z and z <= d+1, 1-2*xi*(cos(2*3.14*((1/2)*z-(1/2)*d)-1/4)-(7/100)*cos(32*3.14*(z-d-1/2))), 1) end proc

(2)

PDE1 :=(diff(f(x,t),t))=1+(1-2*theta((x,t)))*(1/(R(z)^2))*((diff(f(x,t),x,x))+(1/x)*diff(f(x,t),x))+theta((x,t));

PDE1 := diff(f(x, t), t) = 1+(1-2*theta(x, t))*(diff(f(x, t), x, x)+(diff(f(x, t), x))/x)/piecewise(.5 <= z and z <= 1.5, 1-.2*cos(3.140000000*z-1.820000000)+0.1400000000e-1*cos(100.48*z-100.4800000), 1)^2+theta(x, t)

(3)

PDE2 :=2*(diff(theta(x,t),t))=(1/(R(z)^2))*((diff(theta(x,t),x,x))+(1/x)*diff(theta(x,t),x));

PDE2 := 2*(diff(theta(x, t), t)) = (diff(theta(x, t), x, x)+(diff(theta(x, t), x))/x)/piecewise(.5 <= z and z <= 1.5, 1-.2*cos(3.140000000*z-1.820000000)+0.1400000000e-1*cos(100.48*z-100.4800000), 1)^2

(4)

IBC := {D[1](f)(0,t)=0,f(1,t)=0,f(x,0)=0,D[1](theta)(0,t)=0,theta(1,t)=1,theta(x,0)=0};

{f(1, t) = 0, f(x, 0) = 0, theta(1, t) = 1, theta(x, 0) = 0, (D[1](f))(0, t) = 0, (D[1](theta))(0, t) = 0}

(5)

z:=0.98:

NULL

sol:=pdsolve(eval([PDE1,PDE2]),IBC ,numeric, time = t):
sol:-value(f(x,t), output=listprocedure);
fN:=eval( f(x,t), sol:-value(f(x,t), output=listprocedure)):

[x = 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, f(x, 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 ) = (4374356738)  ] ) ] ) INFO := table( [( "depshift" ) = [1, 2], ( "solmat_v" ) = Vector(462, {(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}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(42, 11, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (13, 9) = .0, (13, 10) = .0, (13, 11) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (14, 9) = .0, (14, 10) = .0, (14, 11) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (15, 9) = .0, (15, 10) = .0, (15, 11) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (16, 9) = .0, (16, 10) = .0, (16, 11) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (17, 9) = .0, (17, 10) = .0, (17, 11) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (18, 9) = .0, (18, 10) = .0, (18, 11) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (19, 9) = .0, (19, 10) = .0, (19, 11) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (20, 9) = .0, (20, 10) = .0, (20, 11) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0, (21, 9) = .0, (21, 10) = .0, (21, 11) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (22, 7) = .0, (22, 8) = .0, (22, 9) = .0, (22, 10) = .0, (22, 11) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (23, 7) = .0, (23, 8) = .0, (23, 9) = .0, (23, 10) = .0, (23, 11) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (24, 7) = .0, (24, 8) = .0, (24, 9) = .0, (24, 10) = .0, (24, 11) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (25, 7) = .0, (25, 8) = .0, (25, 9) = .0, (25, 10) = .0, (25, 11) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (26, 7) = .0, (26, 8) = .0, (26, 9) = .0, (26, 10) = .0, (26, 11) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (27, 7) = .0, (27, 8) = .0, (27, 9) = .0, (27, 10) = .0, (27, 11) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (28, 7) = .0, (28, 8) = .0, (28, 9) = .0, (28, 10) = .0, (28, 11) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (29, 7) = .0, (29, 8) = .0, (29, 9) = .0, (29, 10) = .0, (29, 11) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (30, 7) = .0, (30, 8) = .0, (30, 9) = .0, (30, 10) = .0, (30, 11) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (31, 7) = .0, (31, 8) = .0, (31, 9) = .0, (31, 10) = .0, (31, 11) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (32, 7) = .0, (32, 8) = .0, (32, 9) = .0, (32, 10) = .0, (32, 11) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (33, 7) = .0, (33, 8) = .0, (33, 9) = .0, (33, 10) = .0, (33, 11) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (34, 7) = .0, (34, 8) = .0, (34, 9) = .0, (34, 10) = .0, (34, 11) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (35, 7) = .0, (35, 8) = .0, (35, 9) = .0, (35, 10) = .0, (35, 11) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (36, 7) = .0, (36, 8) = .0, (36, 9) = .0, (36, 10) = .0, (36, 11) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (37, 7) = .0, (37, 8) = .0, (37, 9) = .0, (37, 10) = .0, (37, 11) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (38, 7) = .0, (38, 8) = .0, (38, 9) = .0, (38, 10) = .0, (38, 11) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (39, 7) = .0, (39, 8) = .0, (39, 9) = .0, (39, 10) = .0, (39, 11) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (40, 7) = .0, (40, 8) = .0, (40, 9) = .0, (40, 10) = .0, (40, 11) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (41, 7) = .0, (41, 8) = .0, (41, 9) = .0, (41, 10) = .0, (41, 11) = .0, (42, 1) = .0, (42, 2) = .0, (42, 3) = .0, (42, 4) = .0, (42, 5) = .0, (42, 6) = .0, (42, 7) = .0, (42, 8) = .0, (42, 9) = .0, (42, 10) = .0, (42, 11) = .0}, datatype = float[8], order = C_order))]), ( "initialized" ) = false, ( "indepvars" ) = [x, t], ( "explicit" ) = false, ( "depvars" ) = [f, theta], ( "mixed" ) = false, ( "solvec4" ) = Vector(42, {(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}, datatype = float[8]), ( "autonomous" ) = true, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s10, _s11, _s12, _s13, _s2, _s3, _s4, _s5, _s6, _s7, _s8, _s9, xi; _s5 := -2300735754*k; _s6 := -4601471508*k; _s7 := -4000000000*h^2; _s8 := -8000000000*h^2; _s9 := -1150367877*k*h; _s10 := -2000000000*k*h^2; _s11 := -4000000000*k*h^2; _s12 := -_s6-_s7; _s13 := -_s6-_s8; vec[1] := (-(3/2)*v[1]+2*v[3]-(1/2)*v[5])/h; vec[-1+2*n] := v[-1+2*n]; for xi from 2 to n-1 do _s1 := -vp[-3+2*xi]+vp[1+2*xi]; _s4 := vp[-3+2*xi]-2*vp[-1+2*xi]+vp[1+2*xi]; vec[-1+2*xi] := (_s5*_s4*v[2*xi]*x[xi]+_s5*_s4*vp[2*xi]*x[xi]+_s5*v[2*xi]*v[-3+2*xi]*x[xi]-_s6*v[2*xi]*v[-1+2*xi]*x[xi]+_s5*v[2*xi]*v[1+2*xi]*x[xi]+_s5*v[-3+2*xi]*vp[2*xi]*x[xi]-_s6*v[-1+2*xi]*vp[2*xi]*x[xi]+_s5*v[1+2*xi]*vp[2*xi]*x[xi]-_s9*_s1-_s11*x[xi]+_s9*v[-3+2*xi]-_s9*v[1+2*xi]-_s12*v[-1+2*xi]*x[xi]+_s9*_s1*v[2*xi]+_s9*_s1*vp[2*xi]-_s5*_s4*x[xi]-_s9*v[2*xi]*v[-3+2*xi]+_s9*v[2*xi]*v[1+2*xi]-_s9*v[-3+2*xi]*vp[2*xi]+_s9*v[1+2*xi]*vp[2*xi]-_s7*vp[-1+2*xi]*x[xi]-_s10*x[xi]*v[2*xi]-_s10*x[xi]*vp[2*xi]-_s5*v[-3+2*xi]*x[xi]-_s5*v[1+2*xi]*x[xi])/(_s11*x[xi]) end do; vec[2] := (-(3/2)*v[2]+2*v[4]-(1/2)*v[6])/h; vec[2*n] := v[2*n]-1; for xi from 2 to n-1 do _s2 := -vp[2*xi-2]+vp[2+2*xi]; _s3 := vp[2*xi-2]-2*vp[2*xi]+vp[2+2*xi]; vec[2*xi] := -(_s13*v[2*xi]*x[xi]+_s3*_s5*x[xi]+_s5*v[2+2*xi]*x[xi]+_s5*v[2*xi-2]*x[xi]+_s8*vp[2*xi]*x[xi]+_s2*_s9+_s9*v[2+2*xi]-_s9*v[2*xi-2])/(_s11*x[xi]) end do end proc, ( "adjusted" ) = false, ( "solmatrix" ) = Matrix(42, 11, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (13, 9) = .0, (13, 10) = .0, (13, 11) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (14, 9) = .0, (14, 10) = .0, (14, 11) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (15, 9) = .0, (15, 10) = .0, (15, 11) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (16, 9) = .0, (16, 10) = .0, (16, 11) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (17, 9) = .0, (17, 10) = .0, (17, 11) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (18, 9) = .0, (18, 10) = .0, (18, 11) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (19, 9) = .0, (19, 10) = .0, (19, 11) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (20, 9) = .0, (20, 10) = .0, (20, 11) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0, (21, 9) = .0, (21, 10) = .0, (21, 11) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (22, 7) = .0, (22, 8) = .0, (22, 9) = .0, (22, 10) = .0, (22, 11) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (23, 7) = .0, (23, 8) = .0, (23, 9) = .0, (23, 10) = .0, (23, 11) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (24, 7) = .0, (24, 8) = .0, (24, 9) = .0, (24, 10) = .0, (24, 11) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (25, 7) = .0, (25, 8) = .0, (25, 9) = .0, (25, 10) = .0, (25, 11) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (26, 7) = .0, (26, 8) = .0, (26, 9) = .0, (26, 10) = .0, (26, 11) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (27, 7) = .0, (27, 8) = .0, (27, 9) = .0, (27, 10) = .0, (27, 11) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (28, 7) = .0, (28, 8) = .0, (28, 9) = .0, (28, 10) = .0, (28, 11) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (29, 7) = .0, (29, 8) = .0, (29, 9) = .0, (29, 10) = .0, (29, 11) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (30, 7) = .0, (30, 8) = .0, (30, 9) = .0, (30, 10) = .0, (30, 11) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (31, 7) = .0, (31, 8) = .0, (31, 9) = .0, (31, 10) = .0, (31, 11) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (32, 7) = .0, (32, 8) = .0, (32, 9) = .0, (32, 10) = .0, (32, 11) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (33, 7) = .0, (33, 8) = .0, (33, 9) = .0, (33, 10) = .0, (33, 11) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (34, 7) = .0, (34, 8) = .0, (34, 9) = .0, (34, 10) = .0, (34, 11) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (35, 7) = .0, (35, 8) = .0, (35, 9) = .0, (35, 10) = .0, (35, 11) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (36, 7) = .0, (36, 8) = .0, (36, 9) = .0, (36, 10) = .0, (36, 11) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (37, 7) = .0, (37, 8) = .0, (37, 9) = .0, (37, 10) = .0, (37, 11) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (38, 7) = .0, (38, 8) = .0, (38, 9) = .0, (38, 10) = .0, (38, 11) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (39, 7) = .0, (39, 8) = .0, (39, 9) = .0, (39, 10) = .0, (39, 11) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (40, 7) = .0, (40, 8) = .0, (40, 9) = .0, (40, 10) = .0, (40, 11) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (41, 7) = .0, (41, 8) = .0, (41, 9) = .0, (41, 10) = .0, (41, 11) = .0, (42, 1) = .0, (42, 2) = .0, (42, 3) = .0, (42, 4) = .0, (42, 5) = .0, (42, 6) = .0, (42, 7) = .0, (42, 8) = .0, (42, 9) = .0, (42, 10) = .0, (42, 11) = .0}, datatype = float[8], order = C_order), ( "eqndep" ) = [1, 2], ( "timevar" ) = t, ( "intspace" ) = Matrix(21, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0, (8, 1) = .0, (8, 2) = .0, (9, 1) = .0, (9, 2) = .0, (10, 1) = .0, (10, 2) = .0, (11, 1) = .0, (11, 2) = .0, (12, 1) = .0, (12, 2) = .0, (13, 1) = .0, (13, 2) = .0, (14, 1) = .0, (14, 2) = .0, (15, 1) = .0, (15, 2) = .0, (16, 1) = .0, (16, 2) = .0, (17, 1) = .0, (17, 2) = .0, (18, 1) = .0, (18, 2) = .0, (19, 1) = .0, (19, 2) = .0, (20, 1) = .0, (20, 2) = .0, (21, 1) = .0, (21, 2) = .0}, datatype = float[8], order = C_order), ( "solspace" ) = Vector(21, {(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) = 1.0}, datatype = float[8]), ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s10, _s11, _s12, _s13, _s2, _s3, _s4, _s5, _s6, _s7, _s8, _s9, xi; _s3 := -1150367877*h; _s4 := -2300735754*k; _s5 := 4601471508*k; _s6 := 4000000000*h^2; _s7 := -1150367877*k*h; _s8 := 1000000000*k*h^2; _s9 := 2000000000*k*h^2; _s10 := 4000000000*k*h^2; _s11 := (1150367877/1000000000)/h^2; _s12 := -2000000000*h^2-1150367877*k; _s13 := -(1/1000000000)*(1000000000*h^2+1150367877*k)/(k*h^2); mat[4] := (3/2)/h; mat[6] := -2/h; mat[8] := (1/2)/h; mat[22*n-18] := -1; for xi from 2 to n-1 do _s1 := -vp[-3+2*xi]+vp[1+2*xi]; _s2 := vp[-3+2*xi]-2*vp[-1+2*xi]+vp[1+2*xi]; mat[22*xi-17] := (_s2*_s4*x[xi]+_s4*v[-3+2*xi]*x[xi]+_s4*v[1+2*xi]*x[xi]+_s5*v[-1+2*xi]*x[xi]+_s1*_s7-_s7*v[-3+2*xi]+_s7*v[1+2*xi]+_s9*x[xi])/(_s10*x[xi]); mat[22*xi-20] := -(-1+v[2*xi]+vp[2*xi])*(_s3+2300735754*x[xi])/(_s6*x[xi]); mat[22*xi-18] := _s11*v[2*xi]+_s11*vp[2*xi]+_s13; mat[22*xi-16] := (-1+v[2*xi]+vp[2*xi])*(_s3-2300735754*x[xi])/(_s6*x[xi]) end do; mat[15] := (3/2)/h; mat[17] := -2/h; mat[19] := (1/2)/h; mat[-7+22*n] := -1; for xi from 2 to n-1 do mat[-7+22*xi] := _s12/_s8; mat[-5+22*xi] := -(_s4*x[xi]+_s7)/(_s10*x[xi]); mat[-9+22*xi] := -(_s4*x[xi]-_s7)/(_s10*x[xi]) end do end proc, ( "timeidx" ) = 2, ( "totalwidth" ) = 11, ( "spacepts" ) = 21, ( "depeqn" ) = [1, 2], ( "maxords" ) = [2, 1], ( "bandwidth" ) = [2, 6], ( "timestep" ) = 0.500000000000000e-1, ( "minspcpoints" ) = 4, ( "spacevar" ) = x, ( "spacestep" ) = 0.500000000000000e-1, ( "fdepvars" ) = [f(x, t), theta(x, t)], ( "theta" ) = 1/2, ( "spaceadaptive" ) = false, ( "periodic" ) = false, ( "solmat_ne" ) = 0, ( "pts", x ) = [0, 1], ( "solvec5" ) = Vector(42, {(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}, datatype = float[8]), ( "extrabcs" ) = [0, 0], ( "solution" ) = Array(1..3, 1..21, 1..2, {(1, 1, 1) = .0, (1, 1, 2) = .0, (1, 2, 1) = .0, (1, 2, 2) = .0, (1, 3, 1) = .0, (1, 3, 2) = .0, (1, 4, 1) = .0, (1, 4, 2) = .0, (1, 5, 1) = .0, (1, 5, 2) = .0, (1, 6, 1) = .0, (1, 6, 2) = .0, (1, 7, 1) = .0, (1, 7, 2) = .0, (1, 8, 1) = .0, (1, 8, 2) = .0, (1, 9, 1) = .0, (1, 9, 2) = .0, (1, 10, 1) = .0, (1, 10, 2) = .0, (1, 11, 1) = .0, (1, 11, 2) = .0, (1, 12, 1) = .0, (1, 12, 2) = .0, (1, 13, 1) = .0, (1, 13, 2) = .0, (1, 14, 1) = .0, (1, 14, 2) = .0, (1, 15, 1) = .0, (1, 15, 2) = .0, (1, 16, 1) = .0, (1, 16, 2) = .0, (1, 17, 1) = .0, (1, 17, 2) = .0, (1, 18, 1) = .0, (1, 18, 2) = .0, (1, 19, 1) = .0, (1, 19, 2) = .0, (1, 20, 1) = .0, (1, 20, 2) = .0, (1, 21, 1) = .0, (1, 21, 2) = .0, (2, 1, 1) = .0, (2, 1, 2) = .0, (2, 2, 1) = .0, (2, 2, 2) = .0, (2, 3, 1) = .0, (2, 3, 2) = .0, (2, 4, 1) = .0, (2, 4, 2) = .0, (2, 5, 1) = .0, (2, 5, 2) = .0, (2, 6, 1) = .0, (2, 6, 2) = .0, (2, 7, 1) = .0, (2, 7, 2) = .0, (2, 8, 1) = .0, (2, 8, 2) = .0, (2, 9, 1) = .0, (2, 9, 2) = .0, (2, 10, 1) = .0, (2, 10, 2) = .0, (2, 11, 1) = .0, (2, 11, 2) = .0, (2, 12, 1) = .0, (2, 12, 2) = .0, (2, 13, 1) = .0, (2, 13, 2) = .0, (2, 14, 1) = .0, (2, 14, 2) = .0, (2, 15, 1) = .0, (2, 15, 2) = .0, (2, 16, 1) = .0, (2, 16, 2) = .0, (2, 17, 1) = .0, (2, 17, 2) = .0, (2, 18, 1) = .0, (2, 18, 2) = .0, (2, 19, 1) = .0, (2, 19, 2) = .0, (2, 20, 1) = .0, (2, 20, 2) = .0, (2, 21, 1) = .0, (2, 21, 2) = .0, (3, 1, 1) = .0, (3, 1, 2) = .0, (3, 2, 1) = .0, (3, 2, 2) = .0, (3, 3, 1) = .0, (3, 3, 2) = .0, (3, 4, 1) = .0, (3, 4, 2) = .0, (3, 5, 1) = .0, (3, 5, 2) = .0, (3, 6, 1) = .0, (3, 6, 2) = .0, (3, 7, 1) = .0, (3, 7, 2) = .0, (3, 8, 1) = .0, (3, 8, 2) = .0, (3, 9, 1) = .0, (3, 9, 2) = .0, (3, 10, 1) = .0, (3, 10, 2) = .0, (3, 11, 1) = .0, (3, 11, 2) = .0, (3, 12, 1) = .0, (3, 12, 2) = .0, (3, 13, 1) = .0, (3, 13, 2) = .0, (3, 14, 1) = .0, (3, 14, 2) = .0, (3, 15, 1) = .0, (3, 15, 2) = .0, (3, 16, 1) = .0, (3, 16, 2) = .0, (3, 17, 1) = .0, (3, 17, 2) = .0, (3, 18, 1) = .0, (3, 18, 2) = .0, (3, 19, 1) = .0, (3, 19, 2) = .0, (3, 20, 1) = .0, (3, 20, 2) = .0, (3, 21, 1) = .0, (3, 21, 2) = .0}, datatype = float[8], order = C_order), ( "spaceidx" ) = 1, ( "method" ) = theta, ( "eqnords" ) = [[2, 1], [2, 1]], ( "stages" ) = 1, ( "inputargs" ) = [[diff(f(x, t), t) = 1+1.150367877*(1-2*theta(x, t))*(diff(diff(f(x, t), x), x)+(diff(f(x, t), x))/x)+theta(x, t), 2*(diff(theta(x, t), t)) = 1.150367877*(diff(diff(theta(x, t), x), x))+1.150367877*(diff(theta(x, t), x))/x], {f(1, t) = 0, f(x, 0) = 0, theta(1, t) = 1, theta(x, 0) = 0, (D[1](f))(0, t) = 0, (D[1](theta))(0, t) = 0}, time = t], ( "timeadaptive" ) = false, ( "startup_only" ) = false, ( "multidep" ) = [false, false], ( "errorest" ) = false, ( "solvec1" ) = Vector(42, {(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}, datatype = float[8]), ( "IBC" ) = b, ( "solmat_is" ) = 0, ( "dependson" ) = [{1, 2}, {2}], ( "leftwidth" ) = 1, ( "BCS", 2 ) = {[[2, 0, 1], b[2, 0, 1]-1], [[2, 1, 0], b[2, 1, 0]]}, ( "solvec2" ) = Vector(42, {(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}, datatype = float[8]), ( "depdords" ) = [[[2, 1], [0, 0]], [[0, 0], [2, 1]]], ( "erroraccum" ) = true, ( "ICS" ) = [0, 0], ( "BCS", 1 ) = {[[1, 0, 1], b[1, 0, 1]], [[1, 1, 0], b[1, 1, 0]]}, ( "rightwidth" ) = 0, ( "t0" ) = 0, ( "solmat_i1" ) = 0, ( "PDEs" ) = [diff(f(x, t), t)-1-(1150367877/1000000000)*(1-2*theta(x, t))*(diff(diff(f(x, t), x), x)+(diff(f(x, t), x))/x)-theta(x, t), 2*(diff(theta(x, t), t))-(1150367877/1000000000)*(diff(diff(theta(x, t), x), x))-(1150367877/1000000000)*(diff(theta(x, t), x))/x], ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "solvec3" ) = Vector(42, {(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}, datatype = float[8]), ( "banded" ) = true, ( "linear" ) = false, ( "matrixhf" ) = true, ( "depords" ) = [[2, 1], [2, 1]], ( "allocspace" ) = 21, ( "norigdepvars" ) = 2, ( "solmat_i2" ) = 0, ( "vectorhf" ) = true ] ); 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(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .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]

(6)

t := 1;

1

(7)

A1:=x*R(z)*R(z)*(fN)(x, t);

.8692871388*x*fN(x, 1)

(8)

A2:=eval(int(A1, x))+C1;

int(.8692871388*x*fN(x, 1), x)+C1

(9)

W11:=eval(subs(x=0,A2));

Error, (in int) integration range or variable must be specified in the second argument, got 0

 

Find_c1:=solve(W11,C1);

"Find_c1:="

(10)

``


 

Download int_c.mw

Here u is fN(x,t) and t=1.

 

Okey, here is something for you people: the command "pointplot" does not seem to work, however "plot" command does seem to work. Plot command with "style=point" in the syntax seems to give the same result as the books example. Hoever the books example does not give the same results as displayed in the book. 

How is that? Where did i go wrong? 

Could you please help me out? It really feels dumb to do what the book suggests and not getting the same results is a disappointment IMO.. 

k, M, init := 0.9e-3, 670, 30.0

biomass := proc (n::integer) option remember; piecewise(0 < n, biomass(n-1)+k*biomass(n-1)*(M-biomass(n-1)), init) end proc

pts := [seq([n, biomass(n)], n = 0 .. 30)]

pointplot(pts, view = [0 .. 30, 0 .. 700], title = "Biomass")

pointplot([[0, 30.0], [1, 47.280000], [2, 73.77798144], [3, 113.3672328], [4, 170.1607576], [5, 246.7084793], [6, 340.6951260], [7, 441.6684350], [8, 532.4305955], [9, 598.3521395], [10, 636.9357251], [11, 655.8895612], [12, 664.2189618], [13, 667.6748495], [14, 669.0720496], [15, 669.6308287], [16, 669.8533163], [17, 669.9417472], [18, 669.9768706], [19, 669.9908171], [20, 669.9963543], [21, 669.9985526], [22, 669.9994254], [23, 669.9997719], [24, 669.9999094], [25, 669.9999640], [26, 669.9999857], [27, 669.9999943], [28, 669.9999977], [29, 669.9999991], [30, 669.9999996]], view = [0 .. 30, 0 .. 700], title = "Biomass")

(1)

plot(pts, style = point, view = [0 .. 30, 0 .. 700], title = "Biomass")

 

``


So the 2nd line trying to make the plot does seem to work, however i would like to use the "pointplot" command, which does not work. :( 

Greetings,

 

The Function 

Download Discrete_Dynamical_Models_3.mw

 

Worksheet_1.mw

Dear members,

first of all, this is my first question so please excuse me if it is posted in a bad way. Anyway, here is my problem:

 

I am trying to plot a function V(k,i(k)) over the positive real numbers k>0 where i=i(k) is the implicitly defined solution to

    chi(i)-w(k)=0.

Both maps chi(i) and w(k) are relatively simple and well-defined. However, depending on k, two solutions to chi(i)-w(k)=0 coexist, call them i^1(k) and i^2(k). Hence, I want to have two plots:

V(k,i^1(k)) over k as well as V(k,i^2(k)) over k.

Below is my code:

 

 

 

The output is

which corresponds to only one of the solutions. How can I visualize the other solution?

 

Thank you and best regards,

Paul

Bellissima used kripky modules to find the labels for one and two generators. the number of these labels increses to a very large number as we add another level. Can maple help count these lables? and how?

We know that the  showstat()  function can provide some available source codes, but it also provides line numbers.  I need to delete one by one to use it, which is not efficient when I want to copy and modify codes. Is there any way to directly remove those line numbers.

for exampe:

showstat(PlaneDual);

I would like to know how to make a graph like the attached. The Figure IV is showing the changes in the evolution of the rate of technological progress (a topic in economics).

I would like to make a graph exactly like the image attached where it clearly shows the name of the x- and y-axis; the name of the functions; the 45-degree line; the transition from "theta_1" to "theta_2" with the arrows, etc. (In fact, I want to have everything the same from the graph). 

 

I have attached a PDF document with the definition of the functions and the figure itself. I have also attached the image of the figure on this thread. 

 

IMG_633.pdf

Dear everyone, ive been trying to get to learn Maple, and i am using the book: Advanced Problem
Solving Using Maple. 

I am having issues with not getting the same results as the examples. Although i am using the same imput as the examples. So to me that is really odd. I also noted to get the same results as the examples, i had to change the imput to get there. Now this is a bit more complex problem, and i cant figure out where it went wrong. 

Can you help me?

It did seem to produce the answers, however not in the same fashion as the example in the book. I still had to add the values together. No the solution i got is not what i am looking for. 

Greetings,

 

The Function 


 

DDS := a(n+1) = (1+.12*(1/12))*a(n)+1000

a(n+1) = 1.010000000*a(n)+1000

(1)

rsolve({DDS, a(0) = 0}, a(n)); a := unapply(%, n)

proc (n) options operator, arrow; 100000*(101/100)^n-100000 end proc

(2)

plot([-100000+100000*(101/100)^n], n = 0 .. 100, a = 0 .. 200000)

 

pts := {seq([k, a(k)], k = 0 .. 24)}; plot(pts, style = point, title = "Savings Account with Monthly Deposit")

 

rsolve({a(0) = 497.5124378, a(n+1) = -1.01*a(n)+1000}, a(n))

-(11/1005000000)*(-101/100)^n+100000/201

(3)

plot([-(11/1005000000)*(-101/100)^n+100000/201], n = 0 .. 20, a = 0 .. 1000)

 

solve(ev = -1.01*ev+1000, ev)

497.5124378

(4)

rsolve({a(n+1) = .5*a(n)+16}, a(n))

a(0)*(1/2)^n-32*(1/2)^n+32

(5)

rsolve({a(0) = 10, a(n+1) = .5*a(n)+16}, a(n))

-22*(1/2)^n+32

(6)

smartplot(-22*(1/2)^n+32)

 

rsolve({a(0) = 20, a(n+1) = .5*a(n)+16}, a(n))

-12*(1/2)^n+32

(7)

smartplot(-12*(1/2)^n+32)

 

rsolve({a(0) = 32, a(n+1) = .5*a(n)+16}, a(n))

32

(8)

rsolve({a(0) = 50, a(n+1) = .5*a(n)+16}, a(n))

18*(1/2)^n+32

(9)

smartplot(18*(1/2)^n+32)

 

solve(ev = .5*ev+16, ev)

32.

(10)

solve(ev = .5*ev+64, ev)

128.

(11)

rsolve({a(0) = A, a(n+1) = .5*a(n)+64}, a(n)); a := unapply(%, [A, n])

A*(1/2)^n+128-128*(1/2)^n

(12)

inits := [0, 50, 100, 150, 200]

gen := proc (i, j) options operator, arrow; evalf(a(inits, i)) end proc

proc (i, j) options operator, arrow; evalf(a(inits, i)) end proc

(13)

DrugConcTable := Matrix(10, 5, gen)

Matrix(%id = 18446746425282593366)

(14)

help("matrix")

``

``


 

Download Discrete_Dynamical_Models_2.mw

 

We know that it is easier to get all  non-isomorphic graph on n verteices in maple. 

with(GraphTheory):
g:=[NonIsomorphicGraphs(8, output = graphs, outputform = graph)]:
nops(g)

 

But it's not very convenient for planar graphs except for select, especially for special planar graphs (for example,  all triangulations on 12 verices) that have slightly higher number of vertices. In fact, maple has relatively few options for generating special graphs. 

Fortunately, Plantri can do  that at a high rate of speed. Here's the web version of Plantri (http://combos.org/plantri ), so we can enjoy it. More interestingly, I see that Maple has a license to use Nauty  and plantri. https://de.maplesoft.com/support/help/maple/view.aspx?path=License%2fNauty

But I don't know if Maple has any interface functions to use nauty or plantri , and that would be great!

PS: 

  1. Nauty can generate all unlabelled simple graphs on a given number of vertices with various additional properties.
  2. plantri is a program for generation of certain types of planar graph.

 

At age 25, Carrie establishes an individual retirement account (IRA). If she invests #4000 per year for 30years in an ordinary annuity, the account earns 7.75% per year. How much will she have in the account at age 25?

How difficult is it to animate a process using a binary tree for visualization purposes, something that isn't too slow or too complex to implement(as I will then just go with python or something) but also nice to look at(not just boring straight lines).

I'd like to animate, say, a ball moving through different branchings of a multi-tree(binary mainly but ultimately different branchings per node).

 

As an aside. Is there anything like C++ objects/structs in maple that are easy to create using . notation?

 

 

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