J4James

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These are answers submitted by J4James

There were quite a few syntax issues. 

ode.mw

The best is to use piecewise, see for details maple help

restart:with(plots):
p1 := proc (x, y) piecewise(x^2+y^2 <= 1 ,x*y-y^2,0) end proc;
plot3d(p1(x,y), x = -1 .. 1, y = -1 .. 1);

To avoid the error you are getting, just use single quotes

p1 := proc (x, y) if x^2+y^2 <= 1 then x*y-y^2 else 0 end if end proc;

plot3d('p1(x,y)', x = -1 .. 1, y = -1 .. 1);
 

 

As mentioned by Carl Love, your question is unclear. But if you want to see the ouput of the two loops then you need to use printlevel:=3 before the loops. 

The so-called analytical solution you proposed is not satisfying the ode,

Eq:=diff(w(x), x$6)+diff(w(x), x$4)+diff(w(x), x$2)-w(x) = -90;

sol1:=w(x)=C1*sinh(x)+C2*cosh(x)+C3*sin(x)+C4*cos(x)+C5*sin(x)+C6*cos(x)+90;

odetest(sol1, Eq);
 

To verify a solution to an ode, you can use odetest to do so.NULL

restart:

#p1:=1:p2:=1:p3:=1:chi:=1:omega:=2:

Eq:=diff(w(x), x$6)+A*(diff(w(x), x$4))+B*(diff(w(x), x$2))+(-chi*omega^2+C)*w(x) = 0;

diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x)+A*(diff(diff(diff(diff(w(x), x), x), x), x))+B*(diff(diff(w(x), x), x))+(-chi*omega^2+C)*w(x) = 0

(1)

sol:=dsolve(Eq):

simplify(expand(odetest(sol, Eq)))

0

(2)

H:=subs(36*A*B+108*chi*omega^2-108*C-8*A^3+12*sqrt(-12*A^3*chi*omega^2+81*chi^2*omega^4+54*A*B*chi*omega^2+12*A^3*C-3*A^2*B^2-162*C*chi*omega^2-54*A*B*C+12*B^3+81*C^2) = E, (4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)-4*A^2-4*A*E^(1/3)-E^(2/3)+12*B = F, (4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)+4*A^2+4*A*E^(1/3)+E^(2/3)-12*B = G, 4*A^2-2*A*E^(1/3)+E^(2/3)-12*B = S, rhs(sol)):

simplify(subs(E=36*A*B+108*chi*omega^2-108*C-8*A^3+12*sqrt(-12*A^3*chi*omega^2+81*chi^2*omega^4+54*A*B*chi*omega^2+12*A^3*C-3*A^2*B^2-162*C*chi*omega^2-54*A*B*C+12*B^3+81*C^2),subs(S=4*A^2-2*A*E^(1/3)+E^(2/3)-12*B ,subs(G=(4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)+4*A^2+4*A*E^(1/3)+E^(2/3)-12*B,subs(E=36*A*B+108*chi*omega^2-108*C-8*A^3+12*sqrt(-12*A^3*chi*omega^2+81*chi^2*omega^4+54*A*B*chi*omega^2+12*A^3*C-3*A^2*B^2-162*C*chi*omega^2-54*A*B*C+12*B^3+81*C^2),subs(F=(4*I)*A^2*sqrt(3)-I*sqrt(3)*E^(2/3)-(12*I)*B*sqrt(3)-4*A^2-4*A*E^(1/3)-E^(2/3)+12*B,subs(E=36*A*B+108*chi*omega^2-108*C-8*A^3+12*sqrt(-12*A^3*chi*omega^2+81*chi^2*omega^4+54*A*B*chi*omega^2+12*A^3*C-3*A^2*B^2-162*C*chi*omega^2-54*A*B*C+12*B^3+81*C^2),H))))))):

sol1:=w(x)=%:

odetest(sol1, Eq)

0

(3)

 

Download 1.mw

As for as I know, the dsolve has already given you the general solution in compact form.

 

``

restart:

#p1:=1:p2:=1:p3:=1:chi:=1:omega:=2:

Eq:=diff(w(x), x$6)+p1*(diff(w(x), x$4))+p2*(diff(w(x), x$2))+(-chi*omega^2+p3)*w(x) = 0;

diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x)+p1*(diff(diff(diff(diff(w(x), x), x), x), x))+p2*(diff(diff(w(x), x), x))+(-chi*omega^2+p3)*w(x) = 0

(1)

dsolve(Eq):

simplify(expand(rhs(%))):

 

Download 1.mw

You can also opt for the continuation option.

``

restart; with(plots):

Digits:=20:

rho := 1: nu := .1:

B := (diff(psi(u), u$2))/cosh(2*u);

(diff(diff(psi(u), u), u))/cosh(2*u)

(1)

eq0 := (1000-999*lambda)*((diff(B, u$2)+2*(diff(B, u))+B*(4+rho*sqrt(3)*(diff(psi(u), u))/nu)))=0;

(1000-999*lambda)*((diff(diff(diff(diff(psi(u), u), u), u), u))/cosh(2*u)-4*(diff(diff(diff(psi(u), u), u), u))*sinh(2*u)/cosh(2*u)^2+8*(diff(diff(psi(u), u), u))*sinh(2*u)^2/cosh(2*u)^3-4*(diff(diff(psi(u), u), u))/cosh(2*u)+2*(diff(diff(diff(psi(u), u), u), u))/cosh(2*u)-4*(diff(diff(psi(u), u), u))*sinh(2*u)/cosh(2*u)^2+(diff(diff(psi(u), u), u))*(4+10.000000000000000000*3^(1/2)*(diff(psi(u), u)))/cosh(2*u)) = 0

(2)

bc0 := (D(psi))(0.174568e-1) = 0, (D(psi))(-0.174568e-1) = 0, psi(-0.174568e-1) =0.00001, psi(0.174568e-1) = 70;

(D(psi))(0.174568e-1) = 0, (D(psi))(-0.174568e-1) = 0, psi(-0.174568e-1) = 0.1e-4, psi(0.174568e-1) = 70

(3)

sol := dsolve({bc0, eq0},numeric,continuation=lambda);

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 20; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(128, {(1) = -0.174568e-1, (2) = -0.17251103162378087962e-1, (3) = -0.17036624709184358351e-1, (4) = -0.16812672074126164977e-1, (5) = -0.16578234003966653839e-1, (6) = -0.16332433234323016414e-1, (7) = -0.16073983428392461293e-1, (8) = -0.15801561258463532457e-1, (9) = -0.15513674234957133748e-1, (10) = -0.15208217024842576650e-1, (11) = -0.14883280322220009880e-1, (12) = -0.14535767297316221597e-1, (13) = -0.14162681072101637697e-1, (14) = -0.13759843525729559742e-1, (15) = -0.13321821123758797432e-1, (16) = -0.12842836978237005053e-1, (17) = -0.12312852567001972307e-1, (18) = -0.11721189271147690004e-1, (19) = -0.11079305223064061525e-1, (20) = -0.10457430325238769991e-1, (21) = -0.99312096159222472909e-2, (22) = -0.94730041410715511007e-2, (23) = -0.90640093726672464390e-2, (24) = -0.86920574701735620306e-2, (25) = -0.83490208561006733626e-2, (26) = -0.80291139073884427654e-2, (27) = -0.77281607034755589462e-2, (28) = -0.74430030092228383252e-2, (29) = -0.71709467641771166873e-2, (30) = -0.69100227898103097453e-2, (31) = -0.66585029236793552260e-2, (32) = -0.64150689974742742995e-2, (33) = -0.61786023760362610715e-2, (34) = -0.59480459214492490978e-2, (35) = -0.57226867273890877891e-2, (36) = -0.55016834604285143173e-2, (37) = -0.52844896106852147753e-2, (38) = -0.50705083752877653194e-2, (39) = -0.48592133888194511133e-2, (40) = -0.46502299265631499342e-2, (41) = -0.44430454001916904524e-2, (42) = -0.42374066267547216255e-2, (43) = -0.40329434200723257750e-2, (44) = -0.38294276982899588753e-2, (45) = -0.36265990590546761477e-2, (46) = -0.34242307269191457277e-2, (47) = -0.32221791608457029996e-2, (48) = -0.30202481545269902760e-2, (49) = -0.28183615851793465807e-2, (50) = -0.26164175514058865576e-2, (51) = -0.24143727063955446659e-2, (52) = -0.22121762807693560275e-2, (53) = -0.20098292495458971155e-2, (54) = -0.18073341069023237187e-2, (55) = -0.16047071238347836867e-2, (56) = -0.14019641046216212093e-2, (57) = -0.11991464859207074861e-2, (58) = -0.99627526746902237919e-3, (59) = -0.79337732243930487678e-3, (60) = -0.59047498403899505330e-3, (61) = -0.38758313586357609916e-3, (62) = -0.18471139344561720753e-3, (63) = 0.1813782145408320561e-4, (64) = 0.22096658430844446880e-3, (65) = 0.42377922766691728174e-3, (66) = 0.62658512987471114952e-3, (67) = 0.82939111309543734802e-3, (68) = 0.10322042905655174308e-2, (69) = 0.12350260823544019136e-2, (70) = 0.14378562533224464847e-2, (71) = 0.16406860605142892593e-2, (72) = 0.18435060260053441076e-2, (73) = 0.20462876479966181771e-2, (74) = 0.22490129714152004147e-2, (75) = 0.24516541411626073025e-2, (76) = 0.26541784768571959219e-2, (77) = 0.28565585927719557923e-2, (78) = 0.30587722465661955884e-2, (79) = 0.32608138230480603081e-2, (80) = 0.34626999014216343248e-2, (81) = 0.36644548999862057517e-2, (82) = 0.38661375988856476825e-2, (83) = 0.40678149471219755623e-2, (84) = 0.42695704281376818378e-2, (85) = 0.44715822577383154048e-2, (86) = 0.46739735552447157958e-2, (87) = 0.48769868024575304239e-2, (88) = 0.50807865759982434620e-2, (89) = 0.52857162309382958173e-2, (90) = 0.54920460175259721130e-2, (91) = 0.57001107835657224881e-2, (92) = 0.59103201160847526386e-2, (93) = 0.61229985843234965284e-2, (94) = 0.63387550380540543913e-2, (95) = 0.65580295963976511494e-2, (96) = 0.67814898285563795092e-2, (97) = 0.70098318876328365616e-2, (98) = 0.72437846121371975491e-2, (99) = 0.74843571489198749482e-2, (100) = 0.77325422028046730275e-2, (101) = 0.79896418421722844173e-2, (102) = 0.82572272947920953687e-2, (103) = 0.85370903240427087723e-2, (104) = 0.88315995681732085702e-2, (105) = 0.91436922626377864279e-2, (106) = 0.94772192020003361016e-2, (107) = 0.98374774516953594269e-2, (108) = 0.10231363246785292277e-1, (109) = 0.10669175164729475831e-1, (110) = 0.11166511117954299565e-1, (111) = 0.11729949126890680340e-1, (112) = 0.12312281074621879079e-1, (113) = 0.12842294642853717000e-1, (114) = 0.13321644525462615015e-1, (115) = 0.13759754186600172111e-1, (116) = 0.14162628271473617508e-1, (117) = 0.14535758501994290403e-1, (118) = 0.14883278995952821430e-1, (119) = 0.15208216912615347259e-1, (120) = 0.15513674234957133645e-1, (121) = 0.15801561258463532358e-1, (122) = 0.16073983428392461201e-1, (123) = 0.16332433234323016325e-1, (124) = 0.16578234003966653755e-1, (125) = 0.16812672074126164897e-1, (126) = 0.17036624709184358274e-1, (127) = 0.17251103162378087890e-1, (128) = 0.174568e-1}, order = C_order); Y := Matrix(128, 4, {(1, 1) = 0.10000000000000000000e-4, (1, 2) = 0., (1, 3) = -199568.43395915872520, (1, 4) = 79229786.286370996418, (2, 1) = -0.40970770627144214904e-2, (2, 2) = -39.374737269063410713, (2, 3) = -183275.64196722021853, (2, 4) = 79181518.900766500115, (3, 1) = -0.16627365898515301866e-1, (3, 2) = -76.862726142254668408, (3, 3) = -166300.48073087463957, (3, 4) = 79107509.688940821890, (4, 1) = -0.37863307584037904517e-1, (4, 2) = -112.12311367741563357, (4, 3) = -148594.56154666393448, (4, 4) = 79011997.071265827019, (5, 1) = -0.68063082821447896719e-1, (5, 2) = -144.78904542988800780, (5, 3) = -130084.11915881529741, (5, 4) = 78899830.198428404224, (6, 1) = -.10738684218184668506, (6, 2) = -174.38157057015229655, (6, 3) = -110705.57066148692571, (6, 4) = 78776730.466873616183, (7, 1) = -.15592651931264004857, (7, 2) = -200.36384234211527525, (7, 3) = -90362.353013019182840, (7, 4) = 78649088.914136707317, (8, 1) = -.21359823448439217194, (8, 2) = -222.06371100004214465, (8, 3) = -68953.916673056453723, (8, 4) = 78524161.001606875599, (9, 1) = -.28007276739663579927, (9, 2) = -238.66230023150953254, (9, 3) = -46364.784593703711674, (9, 4) = 78409927.887435652249, (10, 1) = -.35476457100561876237, (10, 2) = -249.16836696377530179, (10, 3) = -22429.187675514099846, (10, 4) = 78314732.223044850145, (11, 1) = -.43646490614830770762, (11, 2) = -252.32339524012377469, (11, 3) = 3006.1829833979516210, (11, 4) = 78247098.818633749156, (12, 1) = -.52342182349712560246, (12, 2) = -246.55480115218022902, (12, 3) = 30191.226110645001380, (12, 4) = 78214452.606675554741, (13, 1) = -.61262986513688153090, (13, 2) = -229.84747336188804786, (13, 3) = 59372.055607972976287, (13, 4) = 78221670.568934735363, (14, 1) = -.69955131953886657077, (14, 2) = -199.58232242997926185, (14, 3) = 90890.886350533531754, (14, 4) = 78267665.143961963441, (15, 1) = -.77715700192592853295, (15, 2) = -152.25948833656226742, (15, 3) = 125189.35493940674194, (15, 4) = 78339542.831039114790, (16, 1) = -.83429090247243853263, (16, 2) = -83.306445445547089074, (16, 3) = 162729.32784268007750, (16, 4) = 78401195.725012095487, (17, 1) = -.85364275759704559229, (17, 2) = 13.948721922216291314, (17, 3) = 204279.71166798031384, (17, 4) = 78372321.504166580442, (18, 1) = -.80693034202135334065, (18, 2) = 148.51956677305078090, (18, 3) = 250582.31338443366720, (18, 4) = 78085908.773129380163, (19, 1) = -.65654128982819008675, (19, 2) = 325.40497975204588560, (19, 3) = 300473.81963585052266, (19, 4) = 77255567.235793248749, (20, 1) = -.39299580801152426985, (20, 2) = 527.11284229334415975, (20, 3) = 348070.87273207415358, (20, 4) = 75667041.539389774088, (21, 1) = -0.65600265318465224566e-1, (21, 2) = 720.66101057061333802, (21, 3) = 387354.74664096020784, (21, 4) = 73493764.670722489055, (22, 1) = .30644215327760656609, (22, 2) = 905.77751695942097363, (22, 3) = 420447.57629707826278, (22, 4) = 70817560.841116667434, (23, 1) = .71286519794735143550, (23, 2) = 1083.5795659308292893, (23, 3) = 448798.51102922891869, (23, 4) = 67695509.285329120340, (24, 1) = 1.1475233894291568843, (24, 2) = 1255.1164942300767751, (24, 3) = 473343.84015395161339, (24, 4) = 64170404.731728654118, (25, 1) = 1.6063499595634459001, (25, 2) = 1421.1931534239619461, (25, 3) = 494707.27246085754497, (25, 4) = 60276964.447799332284, (26, 1) = 2.0866371846471389853, (26, 2) = 1582.4681855533055468, (26, 3) = 513329.17183349864941, (26, 4) = 56043327.618631859424, (27, 1) = 2.5863825250936977999, (27, 2) = 1739.4277032161798757, (27, 3) = 529525.23303284572118, (27, 4) = 51494420.316111324072, (28, 1) = 3.1041173465235793518, (28, 2) = 1892.4556957016700893, (28, 3) = 543531.44196304381960, (28, 4) = 46652353.694671256430, (29, 1) = 3.6392387635791876983, (29, 2) = 2041.9916659800070157, (29, 3) = 555538.29264341593988, (29, 4) = 41532442.907839382244, (30, 1) = 4.1910733193584440299, (30, 2) = 2188.2989785408995006, (30, 3) = 565683.20737852098933, (30, 4) = 36151547.304597181025, (31, 1) = 4.7594594065093394244, (31, 2) = 2331.6648531779014226, (31, 3) = 574077.24825772719298, (31, 4) = 30522376.624928891777, (32, 1) = 5.3441456019606851704, (32, 2) = 2472.2622092947237305, (32, 3) = 580802.05753945708820, (32, 4) = 24659263.614907310326, (33, 1) = 5.9450423459067969536, (33, 2) = 2610.2361300547285230, (33, 3) = 585921.36396870178826, (33, 4) = 18575737.383635416962, (34, 1) = 6.5624566163110116599, (34, 2) = 2745.7628165348777208, (34, 3) = 589485.39016478796537, (34, 4) = 12282117.462235983002, (35, 1) = 7.1962289216560997500, (35, 2) = 2878.8664294783455831, (35, 3) = 591528.36774125894316, (35, 4) = 5794356.9878484709135, (36, 1) = 7.8469211172405842212, (36, 2) = 3009.6839316934809459, (36, 3) = 592077.15212822518846, (36, 4) = -877985.52923108262474, (37, 1) = 8.5145666497996675241, (37, 2) = 3138.2054911059996700, (37, 3) = 591148.48836447303006, (37, 4) = -7718875.4077465248652, (38, 1) = 9.1996020513668997697, (38, 2) = 3264.4705357320018145, (38, 3) = 588752.61167629209391, (38, 4) = -14715235.294303611020, (39, 1) = 9.9024849917962869858, (39, 2) = 3388.4898188453719867, (39, 3) = 584893.08882532992642, (39, 4) = -21852903.736003873900, (40, 1) = 10.623359679871107259, (40, 2) = 3510.1930932721339800, (40, 3) = 579570.81500983381132, (40, 4) = -29113144.278884033624, (41, 1) = 11.363010670060219017, (41, 2) = 3629.5939135065045459, (41, 3) = 572778.35715298648803, (41, 4) = -36482152.546211127785, (42, 1) = 12.121450975609129478, (42, 2) = 3746.5556695122611558, (42, 3) = 564511.87853143892543, (42, 4) = -43936775.427910582929, (43, 1) = 12.899218267688784247, (43, 2) = 3861.0069481778401447, (43, 3) = 554761.15385453695424, (43, 4) = -51457397.697086475270, (44, 1) = 13.696407671021213778, (44, 2) = 3972.7918250597807654, (44, 3) = 543520.36336352174285, (44, 4) = -59018352.851009758615, (45, 1) = 14.513298988374500624, (45, 2) = 4081.7674263754625380, (45, 3) = 530781.84569245950467, (45, 4) = -66594041.187264820618, (46, 1) = 15.350093397045444321, (46, 2) = 4187.7656125283695401, (46, 3) = 516539.88326006071082, (46, 4) = -74156352.166474437752, (47, 1) = 16.206677287419931364, (47, 2) = 4290.5683633035717921, (47, 3) = 500796.22969003896618, (47, 4) = -81672692.536938973511, (48, 1) = 17.083171698063099288, (48, 2) = 4389.9787938103994826, (48, 3) = 483551.38948431630385, (48, 4) = -89111028.011168685590, (49, 1) = 17.979179062204023921, (49, 2) = 4485.7353542097500906, (49, 3) = 464819.64179925498950, (49, 4) = -96433547.471452022180, (50, 1) = 18.894389708330709519, (50, 2) = 4577.5875371681182335, (50, 3) = 444618.64538932462736, (50, 4) = -103602248.72248756435, (51, 1) = 19.828197974627180136, (51, 2) = 4665.2579912546611197, (51, 3) = 422978.12548486538161, (51, 4) = -110576149.89894934972, (52, 1) = 20.779988162361096329, (52, 2) = 4748.4759360576142736, (52, 3) = 399934.41206070701713, (52, 4) = -117314007.94583443570, (53, 1) = 21.748851441013411718, (53, 2) = 4826.9552124946923576, (53, 3) = 375537.66851600424838, (53, 4) = -123772750.24880085122, (54, 1) = 22.733812308365361641, (54, 2) = 4900.4196283950424981, (54, 3) = 349847.07301562178956, (54, 4) = -129909733.42580820294, (55, 1) = 23.733769340749409658, (55, 2) = 4968.6010214747457459, (55, 3) = 322932.40703061201505, (55, 4) = -135682880.56329347384, (56, 1) = 24.747565172931711985, (56, 2) = 5031.2471990822652628, (56, 3) = 294872.19633101934400, (56, 4) = -141051659.35811366060, (57, 1) = 25.773857640590647932, (57, 2) = 5088.1168371974082126, (57, 3) = 265757.13095443023623, (57, 4) = -145976969.60980820887, (58, 1) = 26.811354212431916712, (58, 2) = 5138.9959950127779720, (58, 3) = 235683.22175108937135, (58, 4) = -150422894.49980128384, (59, 1) = 27.858686359699544387, (59, 2) = 5183.6914700999997198, (59, 3) = 204754.74139426355812, (59, 4) = -154356462.23256940663, (60, 1) = 28.914468153714793709, (60, 2) = 5222.0350834529413137, (60, 3) = 173081.96059714132628, (60, 4) = -157748323.74318610973, (61, 1) = 29.977318340699603135, (61, 2) = 5253.8847683276720257, (61, 3) = 140779.77087522296740, (61, 4) = -160573128.05512497979, (62, 1) = 31.045855837284835593, (62, 2) = 5279.1242910967848128, (62, 3) = 107967.05304565647724, (62, 4) = -162809739.89729760255, (63, 1) = 32.118716237383111589, (63, 2) = 5297.6634531975832999, (63, 3) = 74765.389525422629916, (63, 4) = -164441458.53559709645, (64, 1) = 33.194543558883294815, (64, 2) = 5309.4374822198027889, (64, 3) = 41298.524229847940154, (64, 4) = -165456121.35860782700, (65, 1) = 34.271983726858234276, (65, 2) = 5314.4067460828659379, (65, 3) = 7691.7807602597236852, (65, 4) = -165846192.60696545272, (66, 1) = 35.349704414738899277, (66, 2) = 5312.5565901699980772, (66, 3) = -25929.338763638324305, (66, 4) = -165608817.70476265941, (67, 1) = 36.426359435366873593, (67, 2) = 5303.8970451542788080, (67, 3) = -59438.820265347857728, (67, 4) = -164745825.09087166903, (68, 1) = 37.500608583851526450, (68, 2) = 5288.4629160283454860, (68, 3) = -92711.531626018404503, (68, 4) = -163263715.81980746141, (69, 1) = 38.571090820374395985, (69, 2) = 5266.3142325082121937, (69, 3) = -125623.17040916130821, (69, 4) = -161173645.30492197382, (70, 1) = 39.636450883807179063, (70, 2) = 5237.5361067620335964, (70, 3) = -158051.87142988418857, (70, 4) = -158491303.50680697163, (71, 1) = 40.695308854623191632, (71, 2) = 5202.2396675607230485, (71, 3) = -189878.06043514794743, (71, 4) = -155236853.12622951911, (72, 1) = 41.746306922485796940, (72, 2) = 5160.5608491518545473, (72, 3) = -220986.64607899748885, (72, 4) = -151434625.88543179513, (73, 1) = 42.788021287130037936, (73, 2) = 5112.6640430747346093, (73, 3) = -251265.18493468224911, (73, 4) = -147113222.17618224455, (74, 1) = 43.819121906807392419, (74, 2) = 5058.7353573810132711, (74, 3) = -280609.31769188032277, (74, 4) = -142304627.97169537232, (75, 1) = 44.838272986712981850, (75, 2) = 4998.9858520645427571, (75, 3) = -308920.46437349546334, (75, 4) = -137044212.41949679025, (76, 1) = 45.844166108347537664, (76, 2) = 4933.6495363269140705, (76, 3) = -336107.39902619917357, (76, 4) = -131370220.89459974528, (77, 1) = 46.835576141266708855, (77, 2) = 4862.9784383223610466, (77, 3) = -362088.22535899920003, (77, 4) = -125323006.39968500967, (78, 1) = 47.811363277630596355, (78, 2) = 4787.2399338611744127, (78, 3) = -386790.65216229630233, (78, 4) = -118944467.64582116871, (79, 1) = 48.770528992962032490, (79, 2) = 4706.7093308840556748, (79, 3) = -410153.43630702480419, (79, 4) = -112277107.29144634934, (80, 1) = 49.712237935631015626, (80, 2) = 4621.6635398804763228, (80, 3) = -432126.58948203532660, (80, 4) = -105363238.01713339795, (81, 1) = 50.635744984070240094, (81, 2) = 4532.3834021059641145, (81, 3) = -452669.22818229872181, (81, 4) = -98244935.274653815403, (82, 1) = 51.540510081004331357, (82, 2) = 4439.1388692474697481, (82, 3) = -471751.62250924828755, (82, 4) = -90962652.145376247944, (83, 1) = 52.426068042140306442, (83, 2) = 4342.1973889377209277, (83, 3) = -489351.57828756614434, (83, 4) = -83555749.468466056537, (84, 1) = 53.292058760342777990, (84, 2) = 4241.8181749573576860, (84, 3) = -505454.52422688034260, (84, 4) = -76061917.459378249872, (85, 1) = 54.138540802228514588, (85, 2) = 4138.2096764805926833, (85, 3) = -520057.97338587733272, (85, 4) = -68514027.328896524821, (86, 1) = 54.965335006274149241, (86, 2) = 4031.6029133642648484, (86, 3) = -533158.51726940923447, (86, 4) = -60945597.835228124133, (87, 1) = 55.772734558338730832, (87, 2) = 3922.1607739394183915, (87, 3) = -544762.94219286979858, (87, 4) = -53384284.986226215255, (88, 1) = 56.560684198127519887, (88, 2) = 3810.0818008657349966, (88, 3) = -554874.44991504234464, (88, 4) = -45859303.870644781604, (89, 1) = 57.329768558266760484, (89, 2) = 3695.4610802419575881, (89, 3) = -563505.27818632543252, (89, 4) = -38392068.232331962121, (90, 1) = 58.080204000539912414, (90, 2) = 3578.4286109907972542, (90, 3) = -570662.16631669897123, (90, 4) = -31005755.642147150808, (91, 1) = 58.812352867074839781, (91, 2) = 3459.0756696694519142, (91, 3) = -576352.38881728282376, (91, 4) = -23720481.969950892002, (92, 1) = 59.526715011154007914, (92, 2) = 3337.4501013785972693, (92, 3) = -580581.73720391088050, (92, 4) = -16553387.854426270493, (93, 1) = 60.223364617194385259, (93, 2) = 3213.6519251563028901, (93, 3) = -583350.66458493831977, (93, 4) = -9524397.4217410379443, (94, 1) = 60.903139994984483063, (94, 2) = 3087.6224569293779809, (94, 3) = -584658.68528226870652, (94, 4) = -2644344.1390369127040, (95, 1) = 61.566119802223377909, (95, 2) = 2959.4124910017601984, (95, 3) = -584497.14138908260671, (95, 4) = 4069544.4840622357071, (96, 1) = 62.212848176643870807, (96, 2) = 2828.9572841628845548, (96, 3) = -582851.56794684874926, (96, 4) = 10605891.383884694483, (97, 1) = 62.843647383909813833, (97, 2) = 2696.2001449833857007, (97, 3) = -579698.72770184113182, (97, 4) = 16952084.509431177276, (98, 1) = 63.458605689106539157, (98, 2) = 2561.0988446828670905, (98, 3) = -575007.08306695030632, (98, 4) = 23094062.140291502835, (99, 1) = 64.058153524095450810, (99, 2) = 2423.4943522058297861, (99, 3) = -568730.30426079332473, (99, 4) = 29021959.875650518920, (100, 1) = 64.642190550556804202, (100, 2) = 2283.2974023900609588, (100, 3) = -560811.48709329354802, (100, 4) = 34721305.957202151927, (101, 1) = 65.210792912242772802, (101, 2) = 2140.3218953530393817, (101, 3) = -551173.26388907403379, (101, 4) = 40179971.176629895292, (102, 1) = 65.763911944852892265, (102, 2) = 1994.3379843030079483, (102, 3) = -539714.54570740250317, (102, 4) = 45385065.236454670053, (103, 1) = 66.301087751757718103, (103, 2) = 1845.1352902344552257, (103, 3) = -526310.39183318747264, (103, 4) = 50320258.889485461863, (104, 1) = 66.821891560568021755, (104, 2) = 1692.3834906622900648, (104, 3) = -510792.50098634375799, (104, 4) = 54969966.436350435685, (105, 1) = 67.325480243036237120, (105, 2) = 1535.7188835201226071, (105, 3) = -492943.53207364773765, (105, 4) = 59315286.140954865975, (106, 1) = 67.810639574819742170, (106, 2) = 1374.6854765624643678, (106, 3) = -472472.66230777975936, (106, 4) = 63334679.159123793826, (107, 1) = 68.275722280779300827, (107, 2) = 1208.6662756106646550, (107, 3) = -448974.82490076370652, (107, 4) = 67003748.321097497761, (108, 1) = 68.717661777042924297, (108, 2) = 1037.1087546282436510, (108, 3) = -421912.49745386732223, (108, 4) = 70288402.121868979924, (109, 1) = 69.132278328751738244, (109, 2) = 859.22448292221933151, (109, 3) = -390484.76670951093833, (109, 4) = 73149504.759327722415, (110, 1) = 69.512822965348038139, (110, 2) = 674.17597282150700204, (110, 3) = -353476.63543537619960, (110, 4) = 75536082.450695257603, (111, 1) = 69.838838766691941356, (111, 2) = 487.11028865175103907, (111, 3) = -310369.92492742857495, (111, 4) = 77335126.299199029735, (112, 1) = 70.072429699353839409, (112, 2) = 319.55540690775932614, (112, 3) = -264986.97886043338964, (112, 4) = 78419235.561758873484, (113, 1) = 70.206528815589471018, (113, 2) = 190.15088597352515630, (113, 3) = -223276.22660451340927, (113, 4) = 78911213.394968970272, (114, 1) = 70.273475482630553734, (114, 2) = 92.197882614399551354, (114, 3) = -185401.54691279964143, (114, 4) = 79078933.117630143868, (115, 1) = 70.297183709006734669, (115, 2) = 18.561924818891215204, (115, 3) = -150751.24146266011587, (115, 4) = 79084009.770655161574, (116, 1) = 70.293289529763212585, (116, 2) = -35.755385568412211413, (116, 3) = -118902.44696422287381, (116, 4) = 79015774.870053469524, (117, 1) = 70.272354896782337171, (117, 2) = -74.623008845506416240, (117, 3) = -89436.090192482603742, (117, 4) = 78923065.811939067189, (118, 1) = 70.241573160016270505, (118, 2) = -100.93994973643336174, (118, 3) = -62024.704495327697415, (118, 4) = 78831452.058624440035, (119, 1) = 70.205950162250387892, (119, 2) = -116.93385964067477112, (119, 3) = -36422.408425548218324, (119, 4) = 78753148.379896427480, (120, 1) = 70.168906683254687586, (120, 2) = -124.38635245548666451, (120, 3) = -12376.325194291574681, (120, 4) = 78692434.464313585526, (121, 1) = 70.132897481624349375, (121, 2) = -124.68900763393249050, (121, 3) = 10271.659640499757685, (121, 4) = 78649321.594563289678, (122, 1) = 70.099575569975957663, (122, 2) = -118.97272953475738135, (122, 3) = 31693.388984177854941, (122, 4) = 78621271.543086419180, (123, 1) = 70.070111790777913216, (123, 2) = -108.15598396967179063, (123, 3) = 52010.699769245208714, (123, 4) = 78604547.411605229346, (124, 1) = 70.045292708216872358, (124, 2) = -92.997257277377527221, (124, 3) = 71330.478126990844444, (124, 4) = 78594859.188542886022, (125, 1) = 70.025619593946742317, (125, 2) = -74.114908704243844311, (125, 3) = 89755.275120174167832, (125, 4) = 78587799.089350407837, (126, 1) = 70.011419309708121558, (126, 2) = -52.043265832552454639, (126, 3) = 107354.32195040972163, (126, 4) = 78579100.367543365586, (127, 1) = 70.002855562258781972, (127, 2) = -27.210812712132175650, (127, 3) = 124206.45305112756964, (127, 4) = 78564753.670005333467, (128, 1) = 70.000000000000000000, (128, 2) = 0., (128, 3) = 140364.74682466066192, (128, 4) = 78541095.275389013526}, order = C_order); YP := Matrix(128, 4, {(1, 1) = 0., (1, 2) = -199568.43395915872520, (1, 3) = 79229786.286370996418, (1, 4) = -169490063.34963251192, (2, 1) = -39.374737269063410713, (2, 2) = -183275.64196722021853, (2, 3) = 79181518.900766500115, (2, 4) = -294251662.94901066183, (3, 1) = -76.862726142254668408, (3, 2) = -166300.48073087463957, (3, 3) = 79107509.688940821890, (3, 4) = -390364522.50194149206, (4, 1) = -112.12311367741563357, (4, 2) = -148594.56154666393448, (4, 3) = 79011997.071265827019, (4, 4) = -457200883.07764691616, (5, 1) = -144.78904542988800780, (5, 2) = -130084.11915881529741, (5, 3) = 78899830.198428404224, (5, 4) = -494469130.51995698873, (6, 1) = -174.38157057015229655, (6, 2) = -110705.57066148692571, (6, 3) = 78776730.466873616183, (6, 4) = -502199927.12515016333, (7, 1) = -200.36384234211527525, (7, 2) = -90362.353013019182840, (7, 3) = 78649088.914136707317, (7, 4) = -480989796.53124429339, (8, 1) = -222.06371100004214465, (8, 2) = -68953.916673056453723, (8, 3) = 78524161.001606875599, (8, 4) = -432176625.42326619009, (9, 1) = -238.66230023150953254, (9, 2) = -46364.784593703711674, (9, 3) = 78409927.887435652249, (9, 4) = -358202568.37660206318, (10, 1) = -249.16836696377530179, (10, 2) = -22429.187675514099846, (10, 3) = 78314732.223044850145, (10, 4) = -262950007.45283772990, (11, 1) = -252.32339524012377469, (11, 2) = 3006.1829833979516210, (11, 3) = 78247098.818633749156, (11, 4) = -152670284.00195610750, (12, 1) = -246.55480115218022902, (12, 2) = 30191.226110645001380, (12, 3) = 78214452.606675554741, (12, 4) = -36595059.163763909385, (13, 1) = -229.84747336188804786, (13, 2) = 59372.055607972976287, (13, 3) = 78221670.568934735363, (13, 4) = 71053901.112319418969, (14, 1) = -199.58232242997926185, (14, 2) = 90890.886350533531754, (14, 3) = 78267665.143961963441, (14, 4) = 149038410.67706356759, (15, 1) = -152.25948833656226742, (15, 2) = 125189.35493940674194, (15, 3) = 78339542.831039114790, (15, 4) = 165110668.13178438760, (16, 1) = -83.306445445547089074, (16, 2) = 162729.32784268007750, (16, 3) = 78401195.725012095487, (16, 4) = 69930423.369991104944, (17, 1) = 13.948721922216291314, (17, 2) = 204279.71166798031384, (17, 3) = 78372321.504166580442, (17, 4) = -213837850.28561894679, (18, 1) = 148.51956677305078090, (18, 2) = 250582.31338443366720, (18, 3) = 78085908.773129380163, (18, 4) = -808123700.10328978708, (19, 1) = 325.40497975204588560, (19, 2) = 300473.81963585052266, (19, 3) = 77255567.235793248749, (19, 4) = -1854909732.3622802592, (20, 1) = 527.11284229334415975, (20, 2) = 348070.87273207415358, (20, 3) = 75667041.539389774088, (20, 4) = -3335532874.0186227050, (21, 1) = 720.66101057061333802, (21, 2) = 387354.74664096020784, (21, 3) = 73493764.670722489055, (21, 4) = -4987902982.9026780865, (22, 1) = 905.77751695942097363, (22, 2) = 420447.57629707826278, (22, 3) = 70817560.841116667434, (22, 4) = -6743237454.0655069434, (23, 1) = 1083.5795659308292893, (23, 2) = 448798.51102922891869, (23, 3) = 67695509.285329120340, (23, 4) = -8563450098.6433969017, (24, 1) = 1255.1164942300767751, (24, 2) = 473343.84015395161339, (24, 3) = 64170404.731728654118, (24, 4) = -10422979219.207281498, (25, 1) = 1421.1931534239619461, (25, 2) = 494707.27246085754497, (25, 3) = 60276964.447799332284, (25, 4) = -12302222815.751315156, (26, 1) = 1582.4681855533055468, (26, 2) = 513329.17183349864941, (26, 3) = 56043327.618631859424, (26, 4) = -14185638004.186805511, (27, 1) = 1739.4277032161798757, (27, 2) = 529525.23303284572118, (27, 3) = 51494420.316111324072, (27, 4) = -16059621258.673044811, (28, 1) = 1892.4556957016700893, (28, 2) = 543531.44196304381960, (28, 3) = 46652353.694671256430, (28, 4) = -17912149186.180869579, (29, 1) = 2041.9916659800070157, (29, 2) = 555538.29264341593988, (29, 3) = 41532442.907839382244, (29, 4) = -19733943526.536590061, (30, 1) = 2188.2989785408995006, (30, 2) = 565683.20737852098933, (30, 3) = 36151547.304597181025, (30, 4) = -21515113121.770864045, (31, 1) = 2331.6648531779014226, (31, 2) = 574077.24825772719298, (31, 3) = 30522376.624928891777, (31, 4) = -23247167468.775794765, (32, 1) = 2472.2622092947237305, (32, 2) = 580802.05753945708820, (32, 3) = 24659263.614907310326, (32, 4) = -24921045116.206185490, (33, 1) = 2610.2361300547285230, (33, 2) = 585921.36396870178826, (33, 3) = 18575737.383635416962, (33, 4) = -26527965055.461064909, (34, 1) = 2745.7628165348777208, (34, 2) = 589485.39016478796537, (34, 3) = 12282117.462235983002, (34, 4) = -28059927694.516235078, (35, 1) = 2878.8664294783455831, (35, 2) = 591528.36774125894316, (35, 3) = 5794356.9878484709135, (35, 4) = -29507514585.112030839, (36, 1) = 3009.6839316934809459, (36, 2) = 592077.15212822518846, (36, 3) = -877985.52923108262474, (36, 4) = -30862772769.766841969, (37, 1) = 3138.2054911059996700, (37, 2) = 591148.48836447303006, (37, 3) = -7718875.4077465248652, (37, 4) = -32116322898.206016175, (38, 1) = 3264.4705357320018145, (38, 2) = 588752.61167629209391, (38, 3) = -14715235.294303611020, (38, 4) = -33259416899.044473448, (39, 1) = 3388.4898188453719867, (39, 2) = 584893.08882532992642, (39, 3) = -21852903.736003873900, (39, 4) = -34283056922.097987467, (40, 1) = 3510.1930932721339800, (40, 2) = 579570.81500983381132, (40, 3) = -29113144.278884033624, (40, 4) = -35177649047.098595704, (41, 1) = 3629.5939135065045459, (41, 2) = 572778.35715298648803, (41, 3) = -36482152.546211127785, (41, 4) = -35934279149.798347563, (42, 1) = 3746.5556695122611558, (42, 2) = 564511.87853143892543, (42, 3) = -43936775.427910582929, (42, 4) = -36543101189.428264024, (43, 1) = 3861.0069481778401447, (43, 2) = 554761.15385453695424, (43, 3) = -51457397.697086475270, (43, 4) = -36994874612.938549081, (44, 1) = 3972.7918250597807654, (44, 2) = 543520.36336352174285, (44, 3) = -59018352.851009758615, (44, 4) = -37280228467.165513051, (45, 1) = 4081.7674263754625380, (45, 2) = 530781.84569245950467, (45, 3) = -66594041.187264820618, (45, 4) = -37390262051.060780133, (46, 1) = 4187.7656125283695401, (46, 2) = 516539.88326006071082, (46, 3) = -74156352.166474437752, (46, 4) = -37316491964.103630092, (47, 1) = 4290.5683633035717921, (47, 2) = 500796.22969003896618, (47, 3) = -81672692.536938973511, (47, 4) = -37051146069.343158318, (48, 1) = 4389.9787938103994826, (48, 2) = 483551.38948431630385, (48, 3) = -89111028.011168685590, (48, 4) = -36587270813.462543416, (49, 1) = 4485.7353542097500906, (49, 2) = 464819.64179925498950, (49, 3) = -96433547.471452022180, (49, 4) = -35919231454.267553632, (50, 1) = 4577.5875371681182335, (50, 2) = 444618.64538932462736, (50, 3) = -103602248.72248756435, (50, 4) = -35042733403.998872341, (51, 1) = 4665.2579912546611197, (51, 2) = 422978.12548486538161, (51, 3) = -110576149.89894934972, (51, 4) = -33955314802.324082520, (52, 1) = 4748.4759360576142736, (52, 2) = 399934.41206070701713, (52, 3) = -117314007.94583443570, (52, 4) = -32656314956.303233795, (53, 1) = 4826.9552124946923576, (53, 2) = 375537.66851600424838, (53, 3) = -123772750.24880085122, (53, 4) = -31147416223.819930788, (54, 1) = 4900.4196283950424981, (54, 2) = 349847.07301562178956, (54, 3) = -129909733.42580820294, (54, 4) = -29432542426.087868177, (55, 1) = 4968.6010214747457459, (55, 2) = 322932.40703061201505, (55, 3) = -135682880.56329347384, (55, 4) = -27518037804.085490078, (56, 1) = 5031.2471990822652628, (56, 2) = 294872.19633101934400, (56, 3) = -141051659.35811366060, (56, 4) = -25412589258.329097790, (57, 1) = 5088.1168371974082126, (57, 2) = 265757.13095443023623, (57, 3) = -145976969.60980820887, (57, 4) = -23127496985.504745615, (58, 1) = 5138.9959950127779720, (58, 2) = 235683.22175108937135, (58, 3) = -150422894.49980128384, (58, 4) = -20676125864.131429374, (59, 1) = 5183.6914700999997198, (59, 2) = 204754.74139426355812, (59, 3) = -154356462.23256940663, (59, 4) = -18074043180.182674735, (60, 1) = 5222.0350834529413137, (60, 2) = 173081.96059714132628, (60, 3) = -157748323.74318610973, (60, 4) = -15338728241.995042176, (61, 1) = 5253.8847683276720257, (61, 2) = 140779.77087522296740, (61, 3) = -160573128.05512497979, (61, 4) = -12489308909.314668143, (62, 1) = 5279.1242910967848128, (62, 2) = 107967.05304565647724, (62, 3) = -162809739.89729760255, (62, 4) = -9546335933.8970521183, (63, 1) = 5297.6634531975832999, (63, 2) = 74765.389525422629916, (63, 3) = -164441458.53559709645, (63, 4) = -6531480189.5576501733, (64, 1) = 5309.4374822198027889, (64, 2) = 41298.524229847940154, (64, 3) = -165456121.35860782700, (64, 4) = -3467281444.2629935778, (65, 1) = 5314.4067460828659379, (65, 2) = 7691.7807602597236852, (65, 3) = -165846192.60696545272, (65, 4) = -376884611.77666629458, (66, 1) = 5312.5565901699980772, (66, 2) = -25929.338763638324305, (66, 3) = -165608817.70476265941, (66, 4) = 2716306047.4052215824, (67, 1) = 5303.8970451542788080, (67, 2) = -59438.820265347857728, (67, 3) = -164745825.09087166903, (67, 4) = 5788816199.4884423649, (68, 1) = 5288.4629160283454860, (68, 2) = -92711.531626018404503, (68, 3) = -163263715.81980746141, (68, 4) = 8817449535.5220891170, (69, 1) = 5266.3142325082121937, (69, 2) = -125623.17040916130821, (69, 3) = -161173645.30492197382, (69, 4) = 11779501041.019209425, (70, 1) = 5237.5361067620335964, (70, 2) = -158051.87142988418857, (70, 3) = -158491303.50680697163, (70, 4) = 14653115568.739089191, (71, 1) = 5202.2396675607230485, (71, 2) = -189878.06043514794743, (71, 3) = -155236853.12622951911, (71, 4) = 17417478753.720280378, (72, 1) = 5160.5608491518545473, (72, 2) = -220986.64607899748885, (72, 3) = -151434625.88543179513, (72, 4) = 20053200466.659673697, (73, 1) = 5112.6640430747346093, (73, 2) = -251265.18493468224911, (73, 3) = -147113222.17618224455, (73, 4) = 22542335911.371495951, (74, 1) = 5058.7353573810132711, (74, 2) = -280609.31769188032277, (74, 3) = -142304627.97169537232, (74, 4) = 24868994896.044312420, (75, 1) = 4998.9858520645427571, (75, 2) = -308920.46437349546334, (75, 3) = -137044212.41949679025, (75, 4) = 27019265196.280280070, (76, 1) = 4933.6495363269140705, (76, 2) = -336107.39902619917357, (76, 3) = -131370220.89459974528, (76, 4) = 28981435959.888520252, (77, 1) = 4862.9784383223610466, (77, 2) = -362088.22535899920003, (77, 3) = -125323006.39968500967, (77, 4) = 30746196227.618684801, (78, 1) = 4787.2399338611744127, (78, 2) = -386790.65216229630233, (78, 3) = -118944467.64582116871, (78, 4) = 32306655056.873854799, (79, 1) = 4706.7093308840556748, (79, 2) = -410153.43630702480419, (79, 3) = -112277107.29144634934, (79, 4) = 33658388064.562798340, (80, 1) = 4621.6635398804763228, (80, 2) = -432126.58948203532660, (80, 3) = -105363238.01713339795, (80, 4) = 34799339627.862926974, (81, 1) = 4532.3834021059641145, (81, 2) = -452669.22818229872181, (81, 3) = -98244935.274653815403, (81, 4) = 35729572136.040938590, (82, 1) = 4439.1388692474697481, (82, 2) = -471751.62250924828755, (82, 3) = -90962652.145376247944, (82, 4) = 36451202698.155216652, (83, 1) = 4342.1973889377209277, (83, 2) = -489351.57828756614434, (83, 3) = -83555749.468466056537, (83, 4) = 36968051409.608042610, (84, 1) = 4241.8181749573576860, (84, 2) = -505454.52422688034260, (84, 3) = -76061917.459378249872, (84, 4) = 37285478219.917814084, (85, 1) = 4138.2096764805926833, (85, 2) = -520057.97338587733272, (85, 3) = -68514027.328896524821, (85, 4) = 37410179157.365619879, (86, 1) = 4031.6029133642648484, (86, 2) = -533158.51726940923447, (86, 3) = -60945597.835228124133, (86, 4) = 37349737968.670538879, (87, 1) = 3922.1607739394183915, (87, 2) = -544762.94219286979858, (87, 3) = -53384284.986226215255, (87, 4) = 37112491180.234271061, (88, 1) = 3810.0818008657349966, (88, 2) = -554874.44991504234464, (88, 3) = -45859303.870644781604, (88, 4) = 36707413889.658199701, (89, 1) = 3695.4610802419575881, (89, 2) = -563505.27818632543252, (89, 3) = -38392068.232331962121, (89, 4) = 36143568252.068958512, (90, 1) = 3578.4286109907972542, (90, 2) = -570662.16631669897123, (90, 3) = -31005755.642147150808, (90, 4) = 35430380909.874131547, (91, 1) = 3459.0756696694519142, (91, 2) = -576352.38881728282376, (91, 3) = -23720481.969950892002, (91, 4) = 34577304395.714463612, (92, 1) = 3337.4501013785972693, (92, 2) = -580581.73720391088050, (92, 3) = -16553387.854426270493, (92, 4) = 33593597649.239347563, (93, 1) = 3213.6519251563028901, (93, 2) = -583350.66458493831977, (93, 3) = -9524397.4217410379443, (93, 4) = 32489068166.382061476, (94, 1) = 3087.6224569293779809, (94, 2) = -584658.68528226870652, (94, 3) = -2644344.1390369127040, (94, 4) = 31272198445.751320936, (95, 1) = 2959.4124910017601984, (95, 2) = -584497.14138908260671, (95, 3) = 4069544.4840622357071, (95, 4) = 29952507603.623945448, (96, 1) = 2828.9572841628845548, (96, 2) = -582851.56794684874926, (96, 3) = 10605891.383884694483, (96, 4) = 28538463666.250504782, (97, 1) = 2696.2001449833857007, (97, 2) = -579698.72770184113182, (97, 3) = 16952084.509431177276, (97, 4) = 27038688244.153361651, (98, 1) = 2561.0988446828670905, (98, 2) = -575007.08306695030632, (98, 3) = 23094062.140291502835, (98, 4) = 25462163539.445974393, (99, 1) = 2423.4943522058297861, (99, 2) = -568730.30426079332473, (99, 3) = 29021959.875650518920, (99, 4) = 23816771156.425307422, (100, 1) = 2283.2974023900609588, (100, 2) = -560811.48709329354802, (100, 3) = 34721305.957202151927, (100, 4) = 22111571873.660638688, (101, 1) = 2140.3218953530393817, (101, 2) = -551173.26388907403379, (101, 3) = 40179971.176629895292, (101, 4) = 20354973005.627089998, (102, 1) = 1994.3379843030079483, (102, 2) = -539714.54570740250317, (102, 3) = 45385065.236454670053, (102, 4) = 18555524198.974425424, (103, 1) = 1845.1352902344552257, (103, 2) = -526310.39183318747264, (103, 3) = 50320258.889485461863, (103, 4) = 16722946901.694117228, (104, 1) = 1692.3834906622900648, (104, 2) = -510792.50098634375799, (104, 3) = 54969966.436350435685, (104, 4) = 14866739547.737319694, (105, 1) = 1535.7188835201226071, (105, 2) = -492943.53207364773765, (105, 3) = 59315286.140954865975, (105, 4) = 12997690721.854220962, (106, 1) = 1374.6854765624643678, (106, 2) = -472472.66230777975936, (106, 3) = 63334679.159123793826, (106, 4) = 11127790132.068576563, (107, 1) = 1208.6662756106646550, (107, 2) = -448974.82490076370652, (107, 3) = 67003748.321097497761, (107, 4) = 9270390613.2051325847, (108, 1) = 1037.1087546282436510, (108, 2) = -421912.49745386732223, (108, 3) = 70288402.121868979924, (108, 4) = 7444062352.2292814348, (109, 1) = 859.22448292221933151, (109, 2) = -390484.76670951093833, (109, 3) = 73149504.759327722415, (109, 4) = 5671185889.3892449104, (110, 1) = 674.17597282150700204, (110, 2) = -353476.63543537619960, (110, 3) = 75536082.450695257603, (110, 4) = 3983215898.1526523451, (111, 1) = 487.11028865175103907, (111, 2) = -310369.92492742857495, (111, 3) = 77335126.299199029735, (111, 4) = 2471148098.6531185155, (112, 1) = 319.55540690775932614, (112, 2) = -264986.97886043338964, (112, 3) = 78419235.561758873484, (112, 4) = 1317525676.1978885398, (113, 1) = 190.15088597352515630, (113, 2) = -223276.22660451340927, (113, 3) = 78911213.394968970272, (113, 4) = 585623718.46936367298, (114, 1) = 92.197882614399551354, (114, 2) = -185401.54691279964143, (114, 3) = 79078933.117630143868, (114, 4) = 146319487.35286039752, (115, 1) = 18.561924818891215204, (115, 2) = -150751.24146266011587, (115, 3) = 79084009.770655161574, (115, 4) = -101013660.61918962910, (116, 1) = -35.755385568412211413, (116, 2) = -118902.44696422287381, (116, 3) = 79015774.870053469524, (116, 4) = -222730537.42168273889, (117, 1) = -74.623008845506416240, (117, 2) = -89436.090192482603742, (117, 3) = 78923065.811939067189, (117, 4) = -264277756.42595237462, (118, 1) = -100.93994973643336174, (118, 2) = -62024.704495327697415, (118, 3) = 78831452.058624440035, (118, 4) = -256726181.79086392076, (119, 1) = -116.93385964067477112, (119, 2) = -36422.408425548218324, (119, 3) = 78753148.379896427480, (119, 4) = -221700116.87572691586, (120, 1) = -124.38635245548666451, (120, 2) = -12376.325194291574681, (120, 3) = 78692434.464313585526, (120, 4) = -174286957.66550610328, (121, 1) = -124.68900763393249050, (121, 2) = 10271.659640499757685, (121, 3) = 78649321.594563289678, (121, 4) = -125175012.52801407368, (122, 1) = -118.97272953475738135, (122, 2) = 31693.388984177854941, (122, 3) = 78621271.543086419180, (122, 4) = -81822599.776293929028, (123, 1) = -108.15598396967179063, (123, 2) = 52010.699769245208714, (123, 3) = 78604547.411605229346, (123, 4) = -49503461.350305658794, (124, 1) = -92.997257277377527221, (124, 2) = 71330.478126990844444, (124, 3) = 78594859.188542886022, (124, 4) = -31864732.004114444814, (125, 1) = -74.114908704243844311, (125, 2) = 89755.275120174167832, (125, 3) = 78587799.089350407837, (125, 4) = -31378603.106406962429, (126, 1) = -52.043265832552454639, (126, 2) = 107354.32195040972163, (126, 3) = 78579100.367543365586, (126, 4) = -49668049.982195336746, (127, 1) = -27.210812712132175650, (127, 2) = 124206.45305112756964, (127, 3) = 78564753.670005333467, (127, 4) = -87736090.470158568134, (128, 1) = 0., (128, 2) = 140364.74682466066192, (128, 3) = 78541095.275389013526, (128, 4) = -146099808.69270020538}, order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 20; outpoint := evalf(x_bvp); X := Vector(128, {(1) = -0.174568e-1, (2) = -0.17251103162378087962e-1, (3) = -0.17036624709184358351e-1, (4) = -0.16812672074126164977e-1, (5) = -0.16578234003966653839e-1, (6) = -0.16332433234323016414e-1, (7) = -0.16073983428392461293e-1, (8) = -0.15801561258463532457e-1, (9) = -0.15513674234957133748e-1, (10) = -0.15208217024842576650e-1, (11) = -0.14883280322220009880e-1, (12) = -0.14535767297316221597e-1, (13) = -0.14162681072101637697e-1, (14) = -0.13759843525729559742e-1, (15) = -0.13321821123758797432e-1, (16) = -0.12842836978237005053e-1, (17) = -0.12312852567001972307e-1, (18) = -0.11721189271147690004e-1, (19) = -0.11079305223064061525e-1, (20) = -0.10457430325238769991e-1, (21) = -0.99312096159222472909e-2, (22) = -0.94730041410715511007e-2, (23) = -0.90640093726672464390e-2, (24) = -0.86920574701735620306e-2, (25) = -0.83490208561006733626e-2, (26) = -0.80291139073884427654e-2, (27) = -0.77281607034755589462e-2, (28) = -0.74430030092228383252e-2, (29) = -0.71709467641771166873e-2, (30) = -0.69100227898103097453e-2, (31) = -0.66585029236793552260e-2, (32) = -0.64150689974742742995e-2, (33) = -0.61786023760362610715e-2, (34) = -0.59480459214492490978e-2, (35) = -0.57226867273890877891e-2, (36) = -0.55016834604285143173e-2, (37) = -0.52844896106852147753e-2, (38) = -0.50705083752877653194e-2, (39) = -0.48592133888194511133e-2, (40) = -0.46502299265631499342e-2, (41) = -0.44430454001916904524e-2, (42) = -0.42374066267547216255e-2, (43) = -0.40329434200723257750e-2, (44) = -0.38294276982899588753e-2, (45) = -0.36265990590546761477e-2, (46) = -0.34242307269191457277e-2, (47) = -0.32221791608457029996e-2, (48) = -0.30202481545269902760e-2, (49) = -0.28183615851793465807e-2, (50) = -0.26164175514058865576e-2, (51) = -0.24143727063955446659e-2, (52) = -0.22121762807693560275e-2, (53) = -0.20098292495458971155e-2, (54) = -0.18073341069023237187e-2, (55) = -0.16047071238347836867e-2, (56) = -0.14019641046216212093e-2, (57) = -0.11991464859207074861e-2, (58) = -0.99627526746902237919e-3, (59) = -0.79337732243930487678e-3, (60) = -0.59047498403899505330e-3, (61) = -0.38758313586357609916e-3, (62) = -0.18471139344561720753e-3, (63) = 0.1813782145408320561e-4, (64) = 0.22096658430844446880e-3, (65) = 0.42377922766691728174e-3, (66) = 0.62658512987471114952e-3, (67) = 0.82939111309543734802e-3, (68) = 0.10322042905655174308e-2, (69) = 0.12350260823544019136e-2, (70) = 0.14378562533224464847e-2, (71) = 0.16406860605142892593e-2, (72) = 0.18435060260053441076e-2, (73) = 0.20462876479966181771e-2, (74) = 0.22490129714152004147e-2, (75) = 0.24516541411626073025e-2, (76) = 0.26541784768571959219e-2, (77) = 0.28565585927719557923e-2, (78) = 0.30587722465661955884e-2, (79) = 0.32608138230480603081e-2, (80) = 0.34626999014216343248e-2, (81) = 0.36644548999862057517e-2, (82) = 0.38661375988856476825e-2, (83) = 0.40678149471219755623e-2, (84) = 0.42695704281376818378e-2, (85) = 0.44715822577383154048e-2, (86) = 0.46739735552447157958e-2, (87) = 0.48769868024575304239e-2, (88) = 0.50807865759982434620e-2, (89) = 0.52857162309382958173e-2, (90) = 0.54920460175259721130e-2, (91) = 0.57001107835657224881e-2, (92) = 0.59103201160847526386e-2, (93) = 0.61229985843234965284e-2, (94) = 0.63387550380540543913e-2, (95) = 0.65580295963976511494e-2, (96) = 0.67814898285563795092e-2, (97) = 0.70098318876328365616e-2, (98) = 0.72437846121371975491e-2, (99) = 0.74843571489198749482e-2, (100) = 0.77325422028046730275e-2, (101) = 0.79896418421722844173e-2, (102) = 0.82572272947920953687e-2, (103) = 0.85370903240427087723e-2, (104) = 0.88315995681732085702e-2, (105) = 0.91436922626377864279e-2, (106) = 0.94772192020003361016e-2, (107) = 0.98374774516953594269e-2, (108) = 0.10231363246785292277e-1, (109) = 0.10669175164729475831e-1, (110) = 0.11166511117954299565e-1, (111) = 0.11729949126890680340e-1, (112) = 0.12312281074621879079e-1, (113) = 0.12842294642853717000e-1, (114) = 0.13321644525462615015e-1, (115) = 0.13759754186600172111e-1, (116) = 0.14162628271473617508e-1, (117) = 0.14535758501994290403e-1, (118) = 0.14883278995952821430e-1, (119) = 0.15208216912615347259e-1, (120) = 0.15513674234957133645e-1, (121) = 0.15801561258463532358e-1, (122) = 0.16073983428392461201e-1, (123) = 0.16332433234323016325e-1, (124) = 0.16578234003966653755e-1, (125) = 0.16812672074126164897e-1, (126) = 0.17036624709184358274e-1, (127) = 0.17251103162378087890e-1, (128) = 0.174568e-1}, order = C_order); Y := Matrix(128, 4, {(1, 1) = 0., (1, 2) = 0., (1, 3) = -0.18824362875150984371e-9, (1, 4) = 0.35767795553101172508e-7, (2, 1) = -0.65890190576540168956e-17, (2, 2) = -0.37821949707699138293e-13, (2, 3) = -0.18077946048910695221e-9, (2, 4) = 0.35612325106802558160e-7, (3, 1) = -0.21788576925069402901e-16, (3, 2) = -0.75620916275590011861e-13, (3, 3) = -0.17290433789507187191e-9, (3, 4) = 0.35361611529209047303e-7, (4, 1) = -0.46342060372976598791e-16, (4, 2) = -0.11339147438973183298e-12, (4, 3) = -0.16482748917582092364e-9, (4, 4) = 0.35006142331326012783e-7, (5, 1) = -0.81152311414087381211e-16, (5, 2) = -0.15072294874898480968e-12, (5, 3) = -0.15670682129535836249e-9, (5, 4) = 0.34572216381092499327e-7, (6, 1) = -0.12725472640767938786e-15, (6, 2) = -0.18789290786888929140e-12, (6, 3) = -0.14812360141654383950e-9, (6, 4) = 0.34083274538939071807e-7, (7, 1) = -0.18531929451711958115e-15, (7, 2) = -0.22460786183563565245e-12, (7, 3) = -0.13937804085352051512e-9, (7, 4) = 0.33520976412764347532e-7, (8, 1) = -0.25713635873998945494e-15, (8, 2) = -0.26093643757551179908e-12, (8, 3) = -0.13033097171075500095e-9, (8, 4) = 0.32910960397152574484e-7, (9, 1) = -0.34360808280792057602e-15, (9, 2) = -0.29657702896419589823e-12, (9, 3) = -0.12099553921041819088e-9, (9, 4) = 0.32254373781021834756e-7, (10, 1) = -0.44711839479127632383e-15, (10, 2) = -0.33133650046002693859e-12, (10, 3) = -0.11136917549872149951e-9, (10, 4) = 0.31580984169646679554e-7, (11, 1) = -0.56896302258067463650e-15, (11, 2) = -0.36534553482479935410e-12, (11, 3) = -0.10145231273548861322e-9, (11, 4) = 0.30915491101552898188e-7, (12, 1) = -0.71164467478890028853e-15, (12, 2) = -0.39808868939234034394e-12, (12, 3) = -0.91162971895216768679e-10, (12, 4) = 0.30287952430901321439e-7, (13, 1) = -0.87797377636255448668e-15, (13, 2) = -0.42915653210529407313e-12, (13, 3) = -0.80479631898406275838e-10, (13, 4) = 0.29697045549328673761e-7, (14, 1) = -0.10713938754124435490e-14, (14, 2) = -0.45885225945864405449e-12, (14, 3) = -0.69332650931303280383e-10, (14, 4) = 0.29285593215116470926e-7, (15, 1) = -0.12962833519016929466e-14, (15, 2) = -0.48624504811315526522e-12, (15, 3) = -0.57502951236783475432e-10, (15, 4) = 0.29052923177216228282e-7, (16, 1) = -0.15579310423491085038e-14, (16, 2) = -0.51085007899409175859e-12, (16, 3) = -0.45076400949346181079e-10, (16, 4) = 0.29092238347282492131e-7, (17, 1) = -0.18639933017712591197e-14, (17, 2) = -0.53189584772267283522e-12, (17, 3) = -0.31314892166313476069e-10, (17, 4) = 0.29602352195385141989e-7, (18, 1) = -0.22195004495140801724e-14, (18, 2) = -0.54582613848231855939e-12, (18, 3) = -0.15891305055029183999e-10, (18, 4) = 0.30796063164593987223e-7, (19, 1) = -0.25809774380406351590e-14, (19, 2) = -0.54163309644791813316e-12, (19, 3) = 0.14860621524218286112e-11, (19, 4) = 0.32554720260686391744e-7, (20, 1) = -0.28872990295996501369e-14, (20, 2) = -0.52549624229921169654e-12, (20, 3) = 0.18347509759135514358e-10, (20, 4) = 0.34334587160320804159e-7, (21, 1) = -0.31643116308038043237e-14, (21, 2) = -0.51405653735045223452e-12, (21, 3) = 0.33661562734104873014e-10, (21, 4) = 0.36335636581862102634e-7, (22, 1) = -0.34093348498117671632e-14, (22, 2) = -0.49927421273492069156e-12, (22, 3) = 0.49021973525154982630e-10, (22, 4) = 0.38408289175541023626e-7, (23, 1) = -0.36243917067661528370e-14, (23, 2) = -0.47981738827543639154e-12, (23, 3) = 0.64012430978329018440e-10, (23, 4) = 0.40395372022388548519e-7, (24, 1) = -0.38132849485063829505e-14, (24, 2) = -0.45821877113246439282e-12, (24, 3) = 0.78811345911981598737e-10, (24, 4) = 0.42238105897319957028e-7, (25, 1) = -0.39785231534963328718e-14, (25, 2) = -0.43065168083065407715e-12, (25, 3) = 0.93437067426650095373e-10, (25, 4) = 0.43866010547191913670e-7, (26, 1) = -0.41241568241575692733e-14, (26, 2) = -0.40159334774339794863e-12, (26, 3) = 0.10777135480070561131e-9, (26, 4) = 0.45233846340939555612e-7, (27, 1) = -0.42501392118262654491e-14, (27, 2) = -0.36827115883737505563e-12, (27, 3) = 0.12190776230778815067e-9, (27, 4) = 0.46312650620708505660e-7, (28, 1) = -0.43602188843548142511e-14, (28, 2) = -0.33281082868787936576e-12, (28, 3) = 0.13578688505899031212e-9, (28, 4) = 0.47092623350792097568e-7, (29, 1) = -0.44556600413302131702e-14, (29, 2) = -0.29513737371405650539e-12, (29, 3) = 0.14917266360838957988e-9, (29, 4) = 0.47546325952020835325e-7, (30, 1) = -0.45358360778067094613e-14, (30, 2) = -0.25552691673442829346e-12, (30, 3) = 0.16229134145230514381e-9, (30, 4) = 0.47649353230207871877e-7, (31, 1) = -0.46034708068510824004e-14, (31, 2) = -0.21429419475784439442e-12, (31, 3) = 0.17493978240512091509e-9, (31, 4) = 0.47401805322564865468e-7, (32, 1) = -0.46556544333604717111e-14, (32, 2) = -0.16805397804551811425e-12, (32, 3) = 0.18710620845806584335e-9, (32, 4) = 0.46773075070255282062e-7, (33, 1) = -0.46972586742483103619e-14, (33, 2) = -0.12481180255405343636e-12, (33, 3) = 0.19892373190815992751e-9, (33, 4) = 0.45764236206446878715e-7, (34, 1) = -0.47260238084079619670e-14, (34, 2) = -0.75258280784530954100e-13, (34, 3) = 0.21024943007054110926e-9, (34, 4) = 0.44334759024656327062e-7, (35, 1) = -0.47430318624333754400e-14, (35, 2) = -0.28488766490115193719e-13, (35, 3) = 0.22081929090201417417e-9, (35, 4) = 0.42497802158272032999e-7, (36, 1) = -0.47496223132215760135e-14, (36, 2) = 0.22976339369734983836e-13, (36, 3) = 0.23105479468946445667e-9, (36, 4) = 0.40238229565432368609e-7, (37, 1) = -0.47428310863020889888e-14, (37, 2) = 0.76032372111566115278e-13, (37, 3) = 0.24036154152833011755e-9, (37, 4) = 0.37543052866247415065e-7, (38, 1) = -0.47248730341443068778e-14, (38, 2) = 0.12878114885950211747e-12, (38, 3) = 0.24901130602754135843e-9, (38, 4) = 0.34401164028402540333e-7, (39, 1) = -0.46962280738620616660e-14, (39, 2) = 0.18412627897171323186e-12, (39, 3) = 0.25671920912159681296e-9, (39, 4) = 0.30810610898796753337e-7, (40, 1) = -0.46662920551728892151e-14, (40, 2) = 0.23756728376044664668e-12, (40, 3) = 0.26366388818532303109e-9, (40, 4) = 0.26758411636425417695e-7, (41, 1) = -0.46050900439428503388e-14, (41, 2) = 0.29403984674689124541e-12, (41, 3) = 0.26971455479428968582e-9, (41, 4) = 0.22250977618456746860e-7, (42, 1) = -0.45398129446389313329e-14, (42, 2) = 0.35375356910166399551e-12, (42, 3) = 0.27480788272029965950e-9, (42, 4) = 0.17301050033286151965e-7, (43, 1) = -0.44591636982680492307e-14, (43, 2) = 0.41254082610634638810e-12, (43, 3) = 0.27855418919730323142e-9, (43, 4) = 0.11928250261844644379e-7, (44, 1) = -0.43627767234825776032e-14, (44, 2) = 0.47207064945325825933e-12, (44, 3) = 0.28131734164303458742e-9, (44, 4) = 0.60957640648106938725e-8, (45, 1) = -0.42796951084707178183e-14, (45, 2) = 0.53047217618764494263e-12, (45, 3) = 0.28268373517748364221e-9, (45, 4) = -0.12510707432899167464e-9, (46, 1) = -0.41744401015349981159e-14, (46, 2) = 0.58974963178844067079e-12, (46, 3) = 0.28257692543738224384e-9, (46, 4) = -0.67438852077060494562e-8, (47, 1) = -0.40517707636238097027e-14, (47, 2) = 0.64941108796985690242e-12, (47, 3) = 0.28119684538393434350e-9, (47, 4) = -0.13700947653987840989e-7, (48, 1) = -0.39124210996243594826e-14, (48, 2) = 0.70960521892438813366e-12, (48, 3) = 0.27835155382609921611e-9, (48, 4) = -0.20946739363110639652e-7, (49, 1) = -0.37375308779718263339e-14, (49, 2) = 0.76829276636146367484e-12, (49, 3) = 0.27371159900984108095e-9, (49, 4) = -0.28466922893996045399e-7, (50, 1) = -0.35985716224494759752e-14, (50, 2) = 0.82577559855688815212e-12, (50, 3) = 0.26746276822004176866e-9, (50, 4) = -0.36166149935205753126e-7, (51, 1) = -0.34058342710901256872e-14, (51, 2) = 0.88105318290621928989e-12, (51, 3) = 0.25957288925885479876e-9, (51, 4) = -0.43904522359300300046e-7, (52, 1) = -0.32337741223338885074e-14, (52, 2) = 0.93682189374818389111e-12, (52, 3) = 0.24999232930368344809e-9, (52, 4) = -0.52017482467967669521e-7, (53, 1) = -0.30224281843500773639e-14, (53, 2) = 0.98997721451147977153e-12, (53, 3) = 0.23847463045101832989e-9, (53, 4) = -0.59707145133475484243e-7, (54, 1) = -0.28136343511988602764e-14, (54, 2) = 0.10394705255868226369e-11, (54, 3) = 0.22534448986020573526e-9, (54, 4) = -0.67400633791592642751e-7, (55, 1) = -0.26037927257537113533e-14, (55, 2) = 0.10859304047175539311e-11, (55, 3) = 0.21043750375536178155e-9, (55, 4) = -0.74901054530081352319e-7, (56, 1) = -0.23722901968233877020e-14, (56, 2) = 0.11295125684379574351e-11, (56, 3) = 0.19393933369046496743e-9, (56, 4) = -0.82025340592350291799e-7, (57, 1) = -0.21275962849855644148e-14, (57, 2) = 0.11701281283416956523e-11, (57, 3) = 0.17576448057545157154e-9, (57, 4) = -0.88742209512713618394e-7, (58, 1) = -0.18655005639431696753e-14, (58, 2) = 0.12067233531278582036e-11, (58, 3) = 0.15608468492221614876e-9, (58, 4) = -0.94765834465056384708e-7, (59, 1) = -0.16245043407194475638e-14, (59, 2) = 0.12388427683473066802e-11, (59, 3) = 0.13517705333898783774e-9, (59, 4) = -0.10021549999332764929e-6, (60, 1) = -0.13714353324622945450e-14, (60, 2) = 0.12660242853551706789e-11, (60, 3) = 0.11306202337216495546e-9, (60, 4) = -0.10508884264650283649e-6, (61, 1) = -0.10753682591384315025e-14, (61, 2) = 0.12886466647361631758e-11, (61, 3) = 0.89745076402175709792e-10, (61, 4) = -0.10913214386355061066e-6, (62, 1) = -0.83392429959667508301e-15, (62, 2) = 0.13069852306719246043e-11, (62, 3) = 0.65735935295556496000e-10, (62, 4) = -0.11217338102231525084e-6, (63, 1) = -0.55201107806505587783e-15, (63, 2) = 0.13179892451120414488e-11, (63, 3) = 0.41113467931541924662e-10, (63, 4) = -0.11447768170798804385e-6, (64, 1) = -0.27097271016428338457e-15, (64, 2) = 0.13234887506825340585e-11, (64, 3) = 0.16062164165213017485e-10, (64, 4) = -0.11586045287507431950e-6, (65, 1) = 0.28097060952353474203e-16, (65, 2) = 0.13251567359111215856e-11, (65, 3) = -0.91547148604933025161e-11, (65, 4) = -0.11587569000797496507e-6, (66, 1) = 0.27933369632881784274e-15, (66, 2) = 0.13209176804378507378e-11, (66, 3) = -0.34348795760126461164e-10, (66, 4) = -0.11542238514837155481e-6, (67, 1) = 0.56117596510936803359e-15, (67, 2) = 0.13093483950304497122e-11, (67, 3) = -0.59280280126912779921e-10, (67, 4) = -0.11373502314574333661e-6, (68, 1) = 0.85398239811872626802e-15, (68, 2) = 0.12943738443106270246e-11, (68, 3) = -0.83736370230433504995e-10, (68, 4) = -0.11130101240159517484e-6, (69, 1) = 0.11049716682910363186e-14, (69, 2) = 0.12729938841659451224e-11, (69, 3) = -0.10750279109263388756e-9, (69, 4) = -0.10775734719497623268e-6, (70, 1) = 0.13795922439572753475e-14, (70, 2) = 0.12482733198088839935e-11, (70, 3) = -0.13037582839172176162e-9, (70, 4) = -0.10329726627171659671e-6, (71, 1) = 0.16458988732898574379e-14, (71, 2) = 0.12168953090361876182e-11, (71, 3) = -0.15210439558837264672e-9, (71, 4) = -0.98148077257576382479e-7, (72, 1) = 0.18727684550051140068e-14, (72, 2) = 0.11818243060082804451e-11, (72, 3) = -0.17257793074331841224e-9, (72, 4) = -0.92347269642503765278e-7, (73, 1) = 0.21385693879272799872e-14, (73, 2) = 0.11438919409564232262e-11, (73, 3) = -0.19159538038901226009e-9, (73, 4) = -0.85832762236708336176e-7, (74, 1) = 0.23672250979636347899e-14, (74, 2) = 0.10994571887991468478e-11, (74, 3) = -0.20911666084702257315e-9, (74, 4) = -0.79027589154380756689e-7, (75, 1) = 0.25817969472719340442e-14, (75, 2) = 0.10522079627390694450e-11, (75, 3) = -0.22514981595461055734e-9, (75, 4) = -0.71391249279380274472e-7, (76, 1) = 0.27952755812283918311e-14, (76, 2) = 0.10017871213272135265e-11, (76, 3) = -0.23934125449622729236e-9, (76, 4) = -0.63796049796106034576e-7, (77, 1) = 0.30106648917828571501e-14, (77, 2) = 0.94793782334250820774e-12, (77, 3) = -0.25190125794196043624e-9, (77, 4) = -0.55815699799912283403e-7, (78, 1) = 0.31933273068623007333e-14, (78, 2) = 0.89469507254316130854e-12, (78, 3) = -0.26250466234479874751e-9, (78, 4) = -0.47846331034140923802e-7, (79, 1) = 0.33713759018904399278e-14, (79, 2) = 0.83644478457205495383e-12, (79, 3) = -0.27131123127314201327e-9, (79, 4) = -0.40011059893261080887e-7, (80, 1) = 0.35339275836075931561e-14, (80, 2) = 0.77900919588057044711e-12, (80, 3) = -0.27835880847915726658e-9, (80, 4) = -0.31967351190533462235e-7, (81, 1) = 0.36755868703068116558e-14, (81, 2) = 0.71794767546752918178e-12, (81, 3) = -0.28389318388094451110e-9, (81, 4) = -0.24158842301245204133e-7, (82, 1) = 0.38279890591465244785e-14, (82, 2) = 0.65718505805177203228e-12, (82, 3) = -0.28749671715619131672e-9, (82, 4) = -0.16546850028682900580e-7, (83, 1) = 0.39520087370927019397e-14, (83, 2) = 0.59736111782153168879e-12, (83, 3) = -0.28961919028386997440e-9, (83, 4) = -0.92377860917904497278e-8, (84, 1) = 0.40717094201900040353e-14, (84, 2) = 0.53527980410820791510e-12, (84, 3) = -0.28999145030363056711e-9, (84, 4) = -0.22524137734433602340e-8, (85, 1) = 0.41718254000397166926e-14, (85, 2) = 0.47554621511949334881e-12, (85, 3) = -0.28921229429652597375e-9, (85, 4) = 0.43916842533031276594e-8, (86, 1) = 0.42534923254507998328e-14, (86, 2) = 0.41457325222169743236e-12, (86, 3) = -0.28681646226698485748e-9, (86, 4) = 0.10597041601164837913e-7, (87, 1) = 0.43428968925408331293e-14, (87, 2) = 0.35472088314127725025e-12, (87, 3) = -0.28340717879971242754e-9, (87, 4) = 0.16406802785493427733e-7, (88, 1) = 0.43946649043026304805e-14, (88, 2) = 0.29398055051046826669e-12, (88, 3) = -0.27858641383444855813e-9, (88, 4) = 0.21744046387987095701e-7, (89, 1) = 0.44351987317187510404e-14, (89, 2) = 0.23616864207153250767e-12, (89, 3) = -0.27270070277341467517e-9, (89, 4) = 0.26643935752243183998e-7, (90, 1) = 0.44804535358679577143e-14, (90, 2) = 0.18054970890989052788e-12, (90, 3) = -0.26600016803639498404e-9, (90, 4) = 0.31074452508031186144e-7, (91, 1) = 0.45223754245758387006e-14, (91, 2) = 0.12343295571430265355e-12, (91, 3) = -0.25806455921380571422e-9, (91, 4) = 0.35055693899608661583e-7, (92, 1) = 0.45323220403615029023e-14, (92, 2) = 0.69088584549209515716e-13, (92, 3) = -0.24943258219534750245e-9, (92, 4) = 0.38558563245278439276e-7, (93, 1) = 0.45409246217207799223e-14, (93, 2) = 0.15742117292048498320e-13, (93, 3) = -0.23996545197375121242e-9, (93, 4) = 0.41598201024133389913e-7, (94, 1) = 0.45410366137106293189e-14, (94, 2) = -0.34820177070264362129e-13, (94, 3) = -0.22970063262947634457e-9, (94, 4) = 0.44198224113721793429e-7, (95, 1) = 0.45075022517720245983e-14, (95, 2) = -0.85351648350751605118e-13, (95, 3) = -0.21904214589085945830e-9, (95, 4) = 0.46354383989331574126e-7, (96, 1) = 0.44747493491479919773e-14, (96, 2) = -0.13318069185325738755e-12, (96, 3) = -0.20759658366573837565e-9, (96, 4) = 0.48085981327011903280e-7, (97, 1) = 0.44368712831180015741e-14, (97, 2) = -0.18139826804797745644e-12, (97, 3) = -0.19564708041275409499e-9, (97, 4) = 0.49374244620964494955e-7, (98, 1) = 0.43922672245678206976e-14, (98, 2) = -0.22384448542885466420e-12, (98, 3) = -0.18308831396516566669e-9, (98, 4) = 0.50292837721294813526e-7, (99, 1) = 0.43231866543134689417e-14, (99, 2) = -0.26649065382742019316e-12, (99, 3) = -0.17013997775110594235e-9, (99, 4) = 0.50782076350413664746e-7, (100, 1) = 0.42379525876154612947e-14, (100, 2) = -0.30597132139203059100e-12, (100, 3) = -0.15695968810714645291e-9, (100, 4) = 0.50927393312497510330e-7, (101, 1) = 0.41432087449417157416e-14, (101, 2) = -0.34556199905906832923e-12, (101, 3) = -0.14316218661513225577e-9, (101, 4) = 0.50707855032269434967e-7, (102, 1) = 0.40482910661655464180e-14, (102, 2) = -0.38010996665638429043e-12, (102, 3) = -0.12897816038440692768e-9, (102, 4) = 0.50129045294280330929e-7, (103, 1) = 0.39307066342479687877e-14, (103, 2) = -0.41279057355188872823e-12, (103, 3) = -0.11466589678016642279e-9, (103, 4) = 0.49229073371105991004e-7, (104, 1) = 0.37908604673925504040e-14, (104, 2) = -0.44244121610263365359e-12, (104, 3) = -0.99969481401623369517e-10, (104, 4) = 0.48026576269199678619e-7, (105, 1) = 0.36448379891240750055e-14, (105, 2) = -0.46968441417356947873e-12, (105, 3) = -0.85057056027202673756e-10, (105, 4) = 0.46536298129896340024e-7, (106, 1) = 0.34456761420794820407e-14, (106, 2) = -0.49438484581974615958e-12, (106, 3) = -0.69625659749430469691e-10, (106, 4) = 0.44819969477099817493e-7, (107, 1) = 0.32697204240719037784e-14, (107, 2) = -0.51121584735639502864e-12, (107, 3) = -0.54346067526673356419e-10, (107, 4) = 0.42859690047242678663e-7, (108, 1) = 0.30435892809231701366e-14, (108, 2) = -0.52679547911465229836e-12, (108, 3) = -0.38565539010048565722e-10, (108, 4) = 0.40741442669996603571e-7, (109, 1) = 0.28002642398652469095e-14, (109, 2) = -0.53660457299856558256e-12, (109, 3) = -0.22612119941690644941e-10, (109, 4) = 0.38515681578183039609e-7, (110, 1) = 0.25154389194708831996e-14, (110, 2) = -0.54081103320882175840e-12, (110, 3) = -0.62890892790393124540e-11, (110, 4) = 0.36309814251313737187e-7, (111, 1) = 0.21917211340446789506e-14, (111, 2) = -0.54081528445236608288e-12, (111, 3) = 0.10561993601949319979e-10, (111, 4) = 0.34267198620798911451e-7, (112, 1) = 0.18716909443030306546e-14, (112, 2) = -0.53174305054402813210e-12, (112, 3) = 0.27585822355513916577e-10, (112, 4) = 0.32551812544320573399e-7, (113, 1) = 0.15595329594715790406e-14, (113, 2) = -0.51232727743823299224e-12, (113, 3) = 0.42452437080993250552e-10, (113, 4) = 0.31444989935579665477e-7, (114, 1) = 0.13112008776690938111e-14, (114, 2) = -0.48792615974145248965e-12, (114, 3) = 0.55914018424981314375e-10, (114, 4) = 0.30878188907746782011e-7, (115, 1) = 0.10679684607930082302e-14, (115, 2) = -0.46045653348834953222e-12, (115, 3) = 0.68468439297498881399e-10, (115, 4) = 0.30721779849568321634e-7, (116, 1) = 0.87986537810635325567e-15, (116, 2) = -0.43072719284131764805e-12, (116, 3) = 0.80091019218347336687e-10, (116, 4) = 0.30797130285275755902e-7, (117, 1) = 0.70129009655084701779e-15, (117, 2) = -0.39914062502236424032e-12, (117, 3) = 0.91076757365108514747e-10, (117, 4) = 0.31059591690516123955e-7, (118, 1) = 0.56098437112185793966e-15, (118, 2) = -0.36612930856947169328e-12, (118, 3) = 0.10154447176568699640e-9, (118, 4) = 0.31455744455151822335e-7, (119, 1) = 0.44970876933879622263e-15, (119, 2) = -0.33194477510830986676e-12, (119, 3) = 0.11161491281237606086e-9, (119, 4) = 0.31869204633084210871e-7, (120, 1) = 0.35037089773759794155e-15, (120, 2) = -0.29681005965325585389e-12, (120, 3) = 0.12125910933184952331e-9, (120, 4) = 0.32351442632532084051e-7, (121, 1) = 0.25180041142286980027e-15, (121, 2) = -0.26099408816665913477e-12, (121, 3) = 0.13054970034281669892e-9, (121, 4) = 0.32827125317853895087e-7, (122, 1) = 0.19561578036964775712e-15, (122, 2) = -0.22458580732495688374e-12, (122, 3) = 0.13951333803252295930e-9, (122, 4) = 0.33293086242947458016e-7, (123, 1) = 0.12535504918701531856e-15, (123, 2) = -0.18771359198481129002e-12, (123, 3) = 0.14817833897675010140e-9, (123, 4) = 0.33732954241753997626e-7, (124, 1) = 0.70220881650522622569e-16, (124, 2) = -0.15048842469280823162e-12, (124, 3) = 0.15657239232410821737e-9, (124, 4) = 0.34109240924724614655e-7, (125, 1) = 0.46740430035744699163e-16, (125, 2) = -0.11303149395145429479e-12, (125, 3) = 0.16467133882010749499e-9, (125, 4) = 0.34459739634040609797e-7, (126, 1) = 0.15149366892734689050e-16, (126, 2) = -0.75426516595514893410e-13, (126, 3) = 0.17253570574873162353e-9, (126, 4) = 0.34719538974710507270e-7, (127, 1) = 0.16746760580094653737e-16, (127, 2) = -0.37731605914719091707e-13, (127, 3) = 0.18013024624076994878e-9, (127, 4) = 0.34918270196913597563e-7, (128, 1) = 0., (128, 2) = 0., (128, 3) = 0.18732189983751400345e-9, (128, 4) = 0.35033456838491134119e-7}, order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[128] elif outpoint = "order" then return 10 elif outpoint = "error" then return 0.11587569000797496507e-6 elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [4, 128, [psi(u), diff(psi(u), u), diff(diff(psi(u), u), u), diff(diff(diff(psi(u), u), u), u)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[128] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[128] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(4, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(128, 4, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(4, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(128, 4, X, Y, outpoint, yout, L, V) end if; [u = outpoint, seq('[psi(u), diff(psi(u), u), diff(diff(psi(u), u), u), diff(diff(diff(psi(u), u), u), u)]'[i] = yout[i], i = 1 .. 4)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[128] elif outpoint = "order" then return 10 elif outpoint = "error" then return 0.11587569000797496507e-6 elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [4, 128, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[128] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[128] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 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}, datatype = float[8], order = C_order); yout := Vector(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(128, 4, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 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.}, order = C_order); yout := Vector(4, {(1) = 0., (2) = 0., (3) = 0., (4) = 0.}); `dsolve/numeric/hermite`(128, 4, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 4)] end proc, (2) = Array(0..0, {}), (3) = [u, psi(u), diff(psi(u), u), diff(diff(psi(u), u), u), diff(diff(diff(psi(u), u), u), u)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [u = res[1], seq('[psi(u), diff(psi(u), u), diff(diff(psi(u), u), u), diff(diff(diff(psi(u), u), u), u)]'[i] = res[i+1], i = 1 .. 4)] catch: error  end try end proc

(4)

odeplot(sol, [u, psi(u)], u = -0.174568e-1 .. 0.174568e-1)

 

odeplot(sol, [u, diff(psi(u),u)], u = -0.174568e-1 .. 0.174568e-1)

 

``

``

``

Download cErrore.mw

In Maple 2016, I have executed your sheet without any problem.

Question.mw 

You can use the many options available  with the 'contourplot' to improve the quaility.

Here I used the `contours=s` and `grid`

contourplot(-(1/2)*y^2-(1/2)*x^2-(1-.3)/sqrt((x+.3)^2+y^2)+((-1)*.3)/sqrt((x-1+.3)^2+y^2), x = -1.5 .. 1.5, y = -1.5 .. 1.5,grid=[60,60],contours=120);

You can get the 2d look from the 3d just by using orientation option

contourplot3d(-(1/2)*y^2-(1/2)*x^2-(1-.3)/sqrt((x+.3)^2+y^2)+((-1)*.3)/sqrt((x-1+.3)^2+y^2), x = -1.5 .. 1.5, y = -1.5 .. 1.5, view = -2 .. -1.3, axes = boxed,style=patchnogrid, grid=[160,160], orientation=[90,360], lightmodel=light4, shading=zhue,  transparency=0.3);
 

 

As mentioned by @ Kitonum, there is no built-in Maple command to find Fourier series of a function.

But you can tell Maple to help you avoid all the integration and summation.

To find a Fourier series of a function, first we need to find the Euler-Fourier formulas (a_m and b_n) and then sum it.  This can be done by writting three procedures like this

``

restart:

a := proc(f,k)
   int(f(x)*cos(k*Pi*x/L),x=-L..L)/L;
end;

proc (f, k) (int(f(x)*cos(k*Pi*x/L), x = -L .. L))/L end proc

(1)

b := proc(f,k)
   int(f(x)*sin(k*Pi*x/L),x=-L..L)/L;
end;

proc (f, k) (int(f(x)*sin(k*Pi*x/L), x = -L .. L))/L end proc

(2)

fss := proc(f,n)
      a(f,0)/2+sum(a(f,k)*cos(k*Pi*x/L)+b(f,k)*sin(k*Pi*x/L),k=1..n);
   end;

proc (f, n) (1/2)*a(f, 0)+sum(a(f, k)*cos(k*Pi*x/L)+b(f, k)*sin(k*Pi*x/L), k = 1 .. n) end proc

(3)

f := x ->x-floor((x+2)/4)*4;L:=2:

proc (x) options operator, arrow; x-4*floor((1/4)*x+1/2) end proc

(4)

a(f,k);

0

(5)

b(f,k);

-4*(k*Pi*cos(k*Pi)-sin(k*Pi))/(k^2*Pi^2)

(6)

fss(f,2);

4*sin((1/2)*Pi*x)/Pi-2*sin(Pi*x)/Pi

(7)

plot({f(x),fss(f,50)},x=-12..12,numpoints=1000,color=[red,green], discont,linestyle=[1,3]);

 

 

``

Download FS.mw

This not my own idea. I got it somewhere on the internet.

restart:with(plots):

x:=2*m*p/(m^2+n^2+p^2);

y:=2*n*p/(m^2+n^2+p^2);

z:=(p^2-(m^2+n^2))/(m^2+n^2+p^2);

p:=2:

plot3d([x,y,z],n=-1..1,m=1..1,grid=[30,30],scaling=constrained,axes=boxed);

f:=x^2+y^2=z^2;

implicitplot(f,n=-1..1,m=-1..1);

Just type it down in maple

restart:
B[d]:=(-d*w[1]+w[3])/(((-2*w[1]+w[3])^2)-((-d*w[1]+w[3])^2)):

B[o]:=(-2*w[1]+w[3])/(((-2*w[1]+w[3])^2)-((-d*w[1]+w[3])^2)):

A[o]:=w[1]*(alpha[o]-c[o]-t[o])+2*w[2]*e[o]:

A[d]:=w[1]*(alpha[d]-c[d]-t[d])+2*w[2]*e[d]:

q[o]:=B[o]*A[o]-B[d]*A[d]:

q[d]:=B[o]*A[d]-B[d]*A[o]:

U[d]:=w[1]*(q[d]*(alpha[d]-q[d]-d*q[o]-c[d]-t[d])-C)+w[2]*(e[d]*q[d]+e[o]*q[o])+w[3]*((1/2)*(q[d]+q[o])^2);

 

restart:

for i to 2 by 1 do
n[i] := (1/2)*i
end do;

for j to 2 by 1 do
eq[j] := diff(f(eta), eta, eta)+(1/(4*eta^2)+(3.*n[j]+1)/(n[j]+1)*(NU/(4*a*eta)-NU*(eta/a)^((n[j]+1)/(2.0*n[j]))/(4*a*eta)))*f(eta) = 0:
end do;

for j to 2 do
dsolve(eq[j]);
end do;

As @Rouben mentioned, you need to post the ODEs you want an answer to. 

Checking the maple help page for dsolve, I found an example which might help

 Define a system of ODEs.

sys_ode := diff(y(t),t) = x(t), diff(x(t),t) = -x(t);


If the unknowns are not specified, all differentiated indeterminate functions in the system are treated as the unknowns of the problem.


dsolve([sys_ode]);


{x(t) = _C2 exp(-t), y(t) = -_C2 exp(-t) + _C1}


Define initial conditions.


ics := x(0)=1, y(1)=0;
ics := x(0) = 1, y(1) = 0


Solve the system of ODEs subject to the initial conditions ics.


dsolve([sys_ode, ics]);

You can then extend for a system of second order ODE's fairly easy. While trying for that if maple is unable to solve analytically your unseen problem then you can use numeric.

GoodLuck


restart:

ODE:=diff(f(eta),eta,eta,eta)-(f(eta)*diff(f(eta),eta,eta)+beta*(1-diff(f(eta),eta)^2))=0;

diff(diff(diff(f(eta), eta), eta), eta)-f(eta)*(diff(diff(f(eta), eta), eta))-beta*(1-(diff(f(eta), eta))^2) = 0

(1)

BCS:=f(0)=0,D(f)(0)=0,D(f)(infinity)=-1;

f(0) = 0, (D(f))(0) = 0, (D(f))(infinity) = -1

(2)

d1:= (f[i+1]-f[i-1])/(2*h);

(1/2)*(f[i+1]-f[i-1])/h

(3)

d2:=(f[i+1]-2*f[i]+f[i-1])/h^2;

(f[i+1]-2*f[i]+f[i-1])/h^2

(4)

d3:= (f[i+1]-3*f[i]+3*f[i-1]-f[i-2])/h^3;

 

(f[i+1]-3*f[i]+3*f[i-1]-f[i-2])/h^3

(5)

ode1:=d3-f[i]*d2-beta(1-d1^2)=0;

(f[i+1]-3*f[i]+3*f[i-1]-f[i-2])/h^3-f[i]*(f[i+1]-2*f[i]+f[i-1])/h^2-beta(-(1/4)*(f[i+1]-f[i-1])^2/h^2+1) = 0

(6)

beta:=0.5;

.5

(7)

h:=0.5;

.5

(8)

ode1;

8.000000000*f[i+1]-24.00000000*f[i]+24.00000000*f[i-1]-8.000000000*f[i-2]-4.000000000*f[i]*(f[i+1]-2*f[i]+f[i-1])-.5 = 0

(9)

eta[0]:=0;

0

(10)

for i from 0 to 9 do
eta[i+1]:=eta[i]+h;
end do:

Using the BCS

f[0]:=0:

f[-1]:=f[1]:

eq[10]:=((f[10]-f[9])/(h))=-1:

for i from 0 to 9 do
eq[i]:=ode1;
end do;

32.00000000*f[1]-8.000000000*f[-2]-.5 = 0

 

8.000000000*f[2]-32.00000000*f[1]-4.000000000*f[1]*(f[2]-2*f[1])-.5 = 0

 

8.000000000*f[3]-24.00000000*f[2]+24.00000000*f[1]-4.000000000*f[2]*(f[3]-2*f[2]+f[1])-.5 = 0

 

8.000000000*f[4]-24.00000000*f[3]+24.00000000*f[2]-8.000000000*f[1]-4.000000000*f[3]*(f[4]-2*f[3]+f[2])-.5 = 0

 

8.000000000*f[5]-24.00000000*f[4]+24.00000000*f[3]-8.000000000*f[2]-4.000000000*f[4]*(f[5]-2*f[4]+f[3])-.5 = 0

 

8.000000000*f[6]-24.00000000*f[5]+24.00000000*f[4]-8.000000000*f[3]-4.000000000*f[5]*(f[6]-2*f[5]+f[4])-.5 = 0

 

8.000000000*f[7]-24.00000000*f[6]+24.00000000*f[5]-8.000000000*f[4]-4.000000000*f[6]*(f[7]-2*f[6]+f[5])-.5 = 0

 

8.000000000*f[8]-24.00000000*f[7]+24.00000000*f[6]-8.000000000*f[5]-4.000000000*f[7]*(f[8]-2*f[7]+f[6])-.5 = 0

 

8.000000000*f[9]-24.00000000*f[8]+24.00000000*f[7]-8.000000000*f[6]-4.000000000*f[8]*(f[9]-2*f[8]+f[7])-.5 = 0

 

8.000000000*f[10]-24.00000000*f[9]+24.00000000*f[8]-8.000000000*f[7]-4.000000000*f[9]*(f[10]-2*f[9]+f[8])-.5 = 0

(11)

soln:=fsolve({eq[0],eq[1],eq[2],eq[3],eq[4],eq[5],eq[6],eq[7],eq[8],eq[9],eq[10]},{f[-2],f[1],f[2],f[3],f[4],f[5],f[6],f[7],f[8],f[9],f[10]});

{f[-2] = -.2970916713, f[1] = -0.5864791783e-1, f[2] = -.1705306168, f[3] = -.2738760311, f[4] = -.3147402162, f[5] = -.2476171394, f[6] = -0.2878916660e-1, f[7] = .4012040661, f[8] = 1.173536498, f[9] = 2.925559378, f[10] = 2.425559378}

(12)

assign(soln);

data:=[seq([eta[0]+i*h,f[i]],i=0..10)];

[[0, 0], [.5, -0.5864791783e-1], [1.0, -.1705306168], [1.5, -.2738760311], [2.0, -.3147402162], [2.5, -.2476171394], [3.0, -0.2878916660e-1], [3.5, .4012040661], [4.0, 1.173536498], [4.5, 2.925559378], [5.0, 2.425559378]]

(13)

 

plot([data],x=eta[0]..10);

 

 


Download FDM_Dbvp_sheet_1.mw

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