Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

I was computing an integral (Running Maple 18 on Windows 10):

The classic lenght of arc Integral of sqrt(1+(dy/dx)^2) dx

In this case, the function was a cartesian circle (x-R)^2+y^2=R^2 isolated as y=sqrt(R^2-(x-R)^2)

When I do the integration, the result of the integral is not correct.
But if I change R for a, the result is correct. Why? This does not make any sense.

R wasn't assigned to any variable. The code was:

Good Integral

[>y:=expand(sqrt(a^2-(x-a)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

Wrong Integral

[>y:=expand(sqrt(R^2-(x-R)^2));
[>f:=expand(simplify(sqrt(1+diff(y,x)^2)));
[>S:=int(f,x)+K;

In fact, any UPPERCASE letter used as the radius gives me the wrong answer whereas any LOWERCASE letter gives me the proper result. Why is this?

Thanks and have a nice day
EDIT: I added a Screenshot

Input:

 a := x^2;
 whattype(x);
 b := x[1]^2;
 whattype(x[1]);
 CodeGeneration[C](a);
 CodeGeneration[C](b);

Output:

Do you know why cg0 =/= x[0]*x[0]?

Hi everyone, how can i plot nonlinear phase portraithere k,w, alpha,K, k, gamma, beta are arbitrary constants and i have three equilibrium points:

I hope the resulting graphics are as follows :

How can I plot these phase portraits? Thanks in advance.

Greetings!

For factorization and computing times purposes, I'd like Maple to not perform this automatic conversion.

whattype(a*b) gives whattype(a*b)

while whattype(a*a) gives whattype(a*a)

Alternatively, a way to factorize 6*x^2+a*x-10 into (a+6*x)*x-10 could do the trick.

Here's a list of the functions I've already tried:

  • factor
  • collect (so coeff too)
  • combine/expand

Any ideas?

Thank you!

Hello. Please help me. I need to calculate the integral (3). This integral has many singular points at which there is convergence in the sense of the principal Cauchy value. The Maple integral itself does not count. I don't understand how to find automatically all the singular points on the integration area. Then, perhaps, it would be possible to split the integral into the sum of integrals by regions, as I roughly wrote in the picture. I want to automate this process, because in fact it is necessary to calculate many integrals of the form (4), where f(x,y) are arbitrary functions that can oscillate strongly, so I don't want to write banal quadrature formulas. I would like to use the means of Maple, since the accuracy will be greater and faster, but we need to somehow bypass the special points. I will be glad of any help. Thank you very much


restart

r1 := 1:

1/1000000

(1)

F1 := 1/(Zp*sqrt(k^2-x^2)*sin(y)+omega*rho1);

1/(46715093.93*(-x^2+1)^(1/2)*sin(y)+1485000)

(2)

Int(F1, x = -k+epsilon .. k-epsilon, y = 0 .. 2*Pi);

Int(1/(46715093.93*(-x^2+1)^(1/2)*sin(y)+1485000), x = -999999/1000000 .. 999999/1000000, y = 0 .. 2*Pi)

(3)

F2 := F1*f(x, y);

f(x, y)/(46715093.93*(-x^2+1)^(1/2)*sin(y)+1485000)

(4)

``

Download Integrate.mw

Is there an option or a tool to know if maple is trying to finish the calculation or if it is in a bucle?

Hi.

I have to make a picture Polynomiograph from metrics such as

m:= Matrix([[1, 2, 3], [4, 5, 6]])

By assigning each number a color as follows.

1 = aquamarine

2 = blue

3 = brown

4 = coral

5 = cyan

6 = black

How should I write the code?

Hello!

I am trying to integrate this function numerically from x=0... 1, by using int and evalf(Int) but maple cannot handle it. Is there another kind of numerical integration?

(2*x-1)^2*(2*n+(5*(2*x-1))*(x-1))*(2*n-5+5*x)*ln(1-(5*(1-x))*x/n)/((1-x)^2*(-2*n-(15*(1-x))*x))

Are there another kind of procedures to do numerical integration?

 

 

I have a printed book copy of Derek Richards' book, Advanced Mathematical Methods With Maple and would like to get the solutions to the problems in the book. Unfortunately the web download is no longer available. I have not been able to locate a copy or to contact Derek Richards directly. 

Can anyone please help?

Thanks

Joe Ladish

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.

 

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?

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