666 jvbasha

javid basha jv

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5 years, 51 days

MaplePrimes Activity


These are questions asked by 666 jvbasha

Hi maple users 

I am working with the PDE solver.

i am receiving a following error

"unable to compute solution for t>HFloat(0.0):" 

Kindly do the needful how to rectify this error.

dumm.mw

Hi, Maple users 

I hope you are doing well.
Here I solved one of the ode problems by dsolve.
But I am getting  "Error, invalid subscript selector" error.
Kindly do the needful to find a solution.
Thank you.

JVB.mw

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.

 

Dear maple users,

A fine day wishes to all.

Here, we have computed the fN(x,t) value by using pdsolve.

We have to integrate the computed value and need to find the values with the sequence of x.

A1:=int(fN(x,1.12),x) 

A2:=seq(A1,x=0..1,0.1)

How to integrate the computed values 

And, How to find the values for the sequence of x.

JVB1.mw
 

restart:

with(PDEtools):

with(plots):

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

{f(x, t)}

(1)

b1:=1.41:d:=0.5/1:xi:=0.1:ea:=0.5:ra:=2:

L:=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):

PDE1 :=ra*(diff(f(x,t),t))=+b1*(1+ea*cos(t))+(1/(L(z)^2))*((diff(f(x,t),x,x))+(1/x)*diff(f(x,t),x));

PDE1 := 2*(diff(f(x, t), t)) = 1.41+.705*cos(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

(2)

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

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

(3)

z:=0.5;

.5

(4)

 

sol:=pdsolve(eval([PDE1]),IBC ,numeric, time = t,spacestep = 0.025, timestep=0.0001):
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 ) = (4336270194)  ] ) ] ) INFO := table( [( "vectorhf" ) = true, ( "solvec2" ) = Vector(41, {(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}, datatype = float[8]), ( "depeqn" ) = [1], ( "solspace" ) = Vector(41, {(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) = 1.0}, datatype = float[8]), ( "spaceadaptive" ) = false, ( "solution" ) = Array(1..3, 1..41, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (1, 22, 1) = .0, (1, 23, 1) = .0, (1, 24, 1) = .0, (1, 25, 1) = .0, (1, 26, 1) = .0, (1, 27, 1) = .0, (1, 28, 1) = .0, (1, 29, 1) = .0, (1, 30, 1) = .0, (1, 31, 1) = .0, (1, 32, 1) = .0, (1, 33, 1) = .0, (1, 34, 1) = .0, (1, 35, 1) = .0, (1, 36, 1) = .0, (1, 37, 1) = .0, (1, 38, 1) = .0, (1, 39, 1) = .0, (1, 40, 1) = .0, (1, 41, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (2, 22, 1) = .0, (2, 23, 1) = .0, (2, 24, 1) = .0, (2, 25, 1) = .0, (2, 26, 1) = .0, (2, 27, 1) = .0, (2, 28, 1) = .0, (2, 29, 1) = .0, (2, 30, 1) = .0, (2, 31, 1) = .0, (2, 32, 1) = .0, (2, 33, 1) = .0, (2, 34, 1) = .0, (2, 35, 1) = .0, (2, 36, 1) = .0, (2, 37, 1) = .0, (2, 38, 1) = .0, (2, 39, 1) = .0, (2, 40, 1) = .0, (2, 41, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0, (3, 22, 1) = .0, (3, 23, 1) = .0, (3, 24, 1) = .0, (3, 25, 1) = .0, (3, 26, 1) = .0, (3, 27, 1) = .0, (3, 28, 1) = .0, (3, 29, 1) = .0, (3, 30, 1) = .0, (3, 31, 1) = .0, (3, 32, 1) = .0, (3, 33, 1) = .0, (3, 34, 1) = .0, (3, 35, 1) = .0, (3, 36, 1) = .0, (3, 37, 1) = .0, (3, 38, 1) = .0, (3, 39, 1) = .0, (3, 40, 1) = .0, (3, 41, 1) = .0}, datatype = float[8], order = C_order), ( "solvec3" ) = Vector(41, {(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}, datatype = float[8]), ( "initialized" ) = false, ( "matrixhf" ) = true, ( "stages" ) = 1, ( "spacevar" ) = x, ( "depshift" ) = [1], ( "spacestep" ) = 0.250000000000000e-1, ( "timeidx" ) = 2, ( "t0" ) = 0, ( "multidep" ) = [false, false], ( "rightwidth" ) = 0, ( "solmat_v" ) = Vector(287, {(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}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(41, 7, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (22, 7) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (23, 7) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (24, 7) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (25, 7) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (26, 7) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (27, 7) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (28, 7) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (29, 7) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (30, 7) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (31, 7) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (32, 7) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (33, 7) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (34, 7) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (35, 7) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (36, 7) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (37, 7) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (38, 7) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (39, 7) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (40, 7) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (41, 7) = .0}, datatype = float[8], order = C_order))]), ( "theta" ) = 1/2, ( "spacepts" ) = 41, ( "solmatrix" ) = Matrix(41, 7, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (22, 7) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (23, 7) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (24, 7) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (25, 7) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (26, 7) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (27, 7) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (28, 7) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (29, 7) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (30, 7) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (31, 7) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (32, 7) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (33, 7) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (34, 7) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (35, 7) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (36, 7) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (37, 7) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (38, 7) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (39, 7) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (40, 7) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (41, 7) = .0}, datatype = float[8], order = C_order), ( "dependson" ) = [{1}], ( "eqndep" ) = [1], ( "timestep" ) = 0.1e-3, ( "leftwidth" ) = 1, ( "IBC" ) = b, ( "BCS", 1 ) = {[[1, 0, 1], b[1, 0, 1]], [[1, 1, 0], b[1, 1, 0]]}, ( "method" ) = theta, ( "erroraccum" ) = true, ( "PDEs" ) = [2*(diff(f(x, t), t))-141/100-(141/200)*cos(t)-(743218889/500000000)*(diff(diff(f(x, t), x), x))-(743218889/500000000)*(diff(f(x, t), x))/x], ( "periodic" ) = false, ( "norigdepvars" ) = 1, ( "linear" ) = true, ( "solmat_i2" ) = 0, ( "solvec5" ) = 0, ( "extrabcs" ) = [0], ( "solmat_is" ) = 0, ( "errorest" ) = false, ( "indepvars" ) = [x, t], ( "solvec1" ) = Vector(41, {(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}, datatype = float[8]), ( "ICS" ) = [0], ( "banded" ) = true, ( "bandwidth" ) = [1, 3], ( "fdepvars" ) = [f(x, t)], ( "solvec4" ) = 0, ( "depvars" ) = [f], ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, _s3, xi; _s1 := -743218889*h; _s2 := 2000000000*h^2; _s3 := (1/500000000)*(1000000000*h^2+743218889*k)/(k*h^2); mat[3] := -(3/2)/h; mat[4] := 2/h; mat[5] := -(1/2)/h; mat[7*n-4] := 1; for xi from 2 to n-1 do mat[7*xi-4] := _s3; mat[7*xi-5] := -(_s1+1486437778*x[xi])/(_s2*x[xi]); mat[7*xi-3] := (_s1-1486437778*x[xi])/(_s2*x[xi]) end do end proc, ( "inputargs" ) = [[2*(diff(f(x, t), t)) = 1.41+.705*cos(t)+1.486437778*(diff(diff(f(x, t), x), x))+1.486437778*(diff(f(x, t), x))/x], {f(1, t) = 0, f(x, 0) = 0, (D[1](f))(0, t) = 0}, time = t, spacestep = 0.25e-1, timestep = 0.1e-3], ( "allocspace" ) = 41, ( "mixed" ) = false, ( "totalwidth" ) = 7, ( "depords" ) = [[2, 1]], ( "solmat_ne" ) = 0, ( "minspcpoints" ) = 4, ( "autonomous" ) = true, ( "explicit" ) = false, ( "depdords" ) = [[[2, 1]]], ( "pts", x ) = [0, 1], ( "eqnords" ) = [[2, 1]], ( "solmat_i1" ) = 0, ( "spaceidx" ) = 1, ( "intspace" ) = Matrix(41, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0, (22, 1) = .0, (23, 1) = .0, (24, 1) = .0, (25, 1) = .0, (26, 1) = .0, (27, 1) = .0, (28, 1) = .0, (29, 1) = .0, (30, 1) = .0, (31, 1) = .0, (32, 1) = .0, (33, 1) = .0, (34, 1) = .0, (35, 1) = .0, (36, 1) = .0, (37, 1) = .0, (38, 1) = .0, (39, 1) = .0, (40, 1) = .0, (41, 1) = .0}, datatype = float[8], order = C_order), ( "startup_only" ) = false, ( "timeadaptive" ) = false, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, _s4, _s5, _s6, _s7, _s8, xi; _s1 := cos(t+(1/2)*k); _s4 := 1486437778*k; _s5 := 4000000000*h^2; _s6 := 743218889*h*k; _s7 := 2000000000*k*h^2; _s8 := 1410000000*k*h^2*(_s1+2); vec[1] := 0; vec[n] := 0; for xi from 2 to n-1 do _s2 := -vp[xi-1]+vp[xi+1]; _s3 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := (_s3*_s4*x[xi]+_s5*vp[xi]*x[xi]+_s2*_s6+_s8*x[xi])/(_s7*x[xi]) end do end proc, ( "maxords" ) = [2, 1], ( "adjusted" ) = false, ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "timevar" ) = t ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := [proc (t, x, u) u[1] end proc]; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2:
", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2:
", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "2nd"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc]

(5)

fN:=eval( f(x,t), sol:-value(f(x,t), output=listprocedure)):

t := 1.2:

A1:= int(fN(x,t),x);

int(fN(x, 1.2), x)

(6)

A2 := seq(A1(x), x = 0.1 .. 1, 0.1);

Error, (in solnproc) unable to compute solution for t>INFO["failtime"]:
unable to store INFO["pts",.1][1] when datatype=float[8]

 

 


 

Download JVB1.mw

 

Dear maple users

A fine day wishes to all 

In my problem, L(z) is a piecewise condition.

L(z):

I have to calculate the f(x,t) value at x=0.71,t=1.12 and z=0.71 for L(z)=0..1.

How to calculate the f(x,t) value.JVB1.mw
 

restart:

with(PDEtools):

with(plots):

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

{f(x, t)}

(1)

b1:=1.41:d:=0.5/1:xi:=0.1:ea:=0.5:ra:=2:

L:=z->piecewise(d<=z,1-2*xi*(cos((2*3.14)*((z-d)*(1/2))-1/4)-(7/100)*cos((32*3.14)*(z-d-1/2))),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, 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))), 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 :=ra*(diff(f(x,t),t))=+b1*(1+ea*cos(t))+(1/(L(z)^2))*((diff(f(x,t),x,x))+(1/x)*diff(f(x,t),x));

PDE1 := 2*(diff(f(x, t), t)) = 1.41+.705*cos(t)+(diff(f(x, t), x, x)+(diff(f(x, t), x))/x)/piecewise(.5 <= z, 1-.2*cos(3.140000000*z-1.820000000)+0.1400000000e-1*cos(100.48*z-100.4800000), z <= 1.5, 1-.2*cos(3.140000000*z-1.820000000)+0.1400000000e-1*cos(100.48*z-100.4800000), 1)^2

(3)

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

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

(4)

z:=0.71;

.71

(5)

sol:=pdsolve(eval([PDE1]),IBC ,numeric, time = t,spacestep = 0.025, timestep=0.0001):
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 ) = (4337711746)  ] ) ] ) INFO := table( [( "indepvars" ) = [x, t], ( "depshift" ) = [1], ( "spacestep" ) = 0.250000000000000e-1, ( "depeqn" ) = [1], ( "solmat_is" ) = 0, ( "solvec3" ) = Vector(41, {(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}, datatype = float[8]), ( "theta" ) = 1/2, ( "matrixhf" ) = true, ( "eqndep" ) = [1], ( "errorest" ) = false, ( "vectorhf" ) = true, ( "spaceadaptive" ) = false, ( "solspace" ) = Vector(41, {(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) = 1.0}, datatype = float[8]), ( "multidep" ) = [false, false], ( "solvec2" ) = Vector(41, {(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}, datatype = float[8]), ( "solmat_i2" ) = 0, ( "intspace" ) = Matrix(41, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0, (22, 1) = .0, (23, 1) = .0, (24, 1) = .0, (25, 1) = .0, (26, 1) = .0, (27, 1) = .0, (28, 1) = .0, (29, 1) = .0, (30, 1) = .0, (31, 1) = .0, (32, 1) = .0, (33, 1) = .0, (34, 1) = .0, (35, 1) = .0, (36, 1) = .0, (37, 1) = .0, (38, 1) = .0, (39, 1) = .0, (40, 1) = .0, (41, 1) = .0}, datatype = float[8], order = C_order), ( "solmat_i1" ) = 0, ( "erroraccum" ) = true, ( "solmatrix" ) = Matrix(41, 7, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (22, 7) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (23, 7) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (24, 7) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (25, 7) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (26, 7) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (27, 7) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (28, 7) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (29, 7) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (30, 7) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (31, 7) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (32, 7) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (33, 7) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (34, 7) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (35, 7) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (36, 7) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (37, 7) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (38, 7) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (39, 7) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (40, 7) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (41, 7) = .0}, datatype = float[8], order = C_order), ( "leftwidth" ) = 1, ( "adjusted" ) = false, ( "totalwidth" ) = 7, ( "solmat_v" ) = Vector(287, {(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}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(41, 7, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (22, 7) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (23, 7) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (24, 7) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (25, 7) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (26, 7) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (27, 7) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (28, 7) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (29, 7) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (30, 7) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (31, 7) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (32, 7) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (33, 7) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (34, 7) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (35, 7) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (36, 7) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (37, 7) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (38, 7) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (39, 7) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (40, 7) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (41, 7) = .0}, datatype = float[8], order = C_order))]), ( "stages" ) = 1, ( "solmat_ne" ) = 0, ( "allocspace" ) = 41, ( "PDEs" ) = [2*(diff(f(x, t), t))-141/100-(141/200)*cos(t)-(1533816497/1000000000)*(diff(diff(f(x, t), x), x))-(1533816497/1000000000)*(diff(f(x, t), x))/x], ( "method" ) = theta, ( "minspcpoints" ) = 4, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, _s4, _s5, _s6, _s7, _s8, xi; _s1 := cos(t+(1/2)*k); _s4 := 3067632994*k; _s5 := 8000000000*h^2; _s6 := 1533816497*h*k; _s7 := 4000000000*k*h^2; _s8 := 2820000000*k*h^2*(_s1+2); vec[1] := 0; vec[n] := 0; for xi from 2 to n-1 do _s2 := -vp[xi-1]+vp[xi+1]; _s3 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := (_s3*_s4*x[xi]+_s5*vp[xi]*x[xi]+_s2*_s6+_s8*x[xi])/(_s7*x[xi]) end do end proc, ( "t0" ) = 0, ( "rightwidth" ) = 0, ( "solvec1" ) = Vector(41, {(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}, datatype = float[8]), ( "linear" ) = true, ( "timeidx" ) = 2, ( "spacevar" ) = x, ( "timeadaptive" ) = false, ( "startup_only" ) = false, ( "initialized" ) = false, ( "solvec4" ) = 0, ( "solution" ) = Array(1..3, 1..41, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (1, 22, 1) = .0, (1, 23, 1) = .0, (1, 24, 1) = .0, (1, 25, 1) = .0, (1, 26, 1) = .0, (1, 27, 1) = .0, (1, 28, 1) = .0, (1, 29, 1) = .0, (1, 30, 1) = .0, (1, 31, 1) = .0, (1, 32, 1) = .0, (1, 33, 1) = .0, (1, 34, 1) = .0, (1, 35, 1) = .0, (1, 36, 1) = .0, (1, 37, 1) = .0, (1, 38, 1) = .0, (1, 39, 1) = .0, (1, 40, 1) = .0, (1, 41, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (2, 22, 1) = .0, (2, 23, 1) = .0, (2, 24, 1) = .0, (2, 25, 1) = .0, (2, 26, 1) = .0, (2, 27, 1) = .0, (2, 28, 1) = .0, (2, 29, 1) = .0, (2, 30, 1) = .0, (2, 31, 1) = .0, (2, 32, 1) = .0, (2, 33, 1) = .0, (2, 34, 1) = .0, (2, 35, 1) = .0, (2, 36, 1) = .0, (2, 37, 1) = .0, (2, 38, 1) = .0, (2, 39, 1) = .0, (2, 40, 1) = .0, (2, 41, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0, (3, 22, 1) = .0, (3, 23, 1) = .0, (3, 24, 1) = .0, (3, 25, 1) = .0, (3, 26, 1) = .0, (3, 27, 1) = .0, (3, 28, 1) = .0, (3, 29, 1) = .0, (3, 30, 1) = .0, (3, 31, 1) = .0, (3, 32, 1) = .0, (3, 33, 1) = .0, (3, 34, 1) = .0, (3, 35, 1) = .0, (3, 36, 1) = .0, (3, 37, 1) = .0, (3, 38, 1) = .0, (3, 39, 1) = .0, (3, 40, 1) = .0, (3, 41, 1) = .0}, datatype = float[8], order = C_order), ( "norigdepvars" ) = 1, ( "mixed" ) = false, ( "bandwidth" ) = [1, 3], ( "extrabcs" ) = [0], ( "depdords" ) = [[[2, 1]]], ( "solvec5" ) = 0, ( "spacepts" ) = 41, ( "spaceidx" ) = 1, ( "timestep" ) = 0.1e-3, ( "inputargs" ) = [[2*(diff(f(x, t), t)) = 1.41+.705*cos(t)+1.533816497*(diff(diff(f(x, t), x), x))+1.533816497*(diff(f(x, t), x))/x], {f(1, t) = 0, f(x, 0) = 0, (D[1](f))(0, t) = 0}, time = t, spacestep = 0.25e-1, timestep = 0.1e-3], ( "maxords" ) = [2, 1], ( "timevar" ) = t, ( "BCS", 1 ) = {[[1, 0, 1], b[1, 0, 1]], [[1, 1, 0], b[1, 1, 0]]}, ( "eqnords" ) = [[2, 1]], ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "periodic" ) = false, ( "depords" ) = [[2, 1]], ( "ICS" ) = [0], ( "fdepvars" ) = [f(x, t)], ( "depvars" ) = [f], ( "dependson" ) = [{1}], ( "autonomous" ) = true, ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, _s3, xi; _s1 := -1533816497*h; _s2 := 4000000000*h^2; _s3 := (1/1000000000)*(2000000000*h^2+1533816497*k)/(k*h^2); mat[3] := -(3/2)/h; mat[4] := 2/h; mat[5] := -(1/2)/h; mat[7*n-4] := 1; for xi from 2 to n-1 do mat[7*xi-4] := _s3; mat[7*xi-5] := -(_s1+3067632994*x[xi])/(_s2*x[xi]); mat[7*xi-3] := (_s1-3067632994*x[xi])/(_s2*x[xi]) end do end proc, ( "explicit" ) = false, ( "banded" ) = true, ( "pts", x ) = [0, 1], ( "IBC" ) = b ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := [proc (t, x, u) u[1] end proc]; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2:
", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2:
", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "2nd"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc]

(6)

fN:=eval( f(x,t), sol:-value(f(x,t), output=listprocedure)):

 


 

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