MaplePrimes Questions

Hi

I was trying to find the inverse of a function where the domain has been restricted. For example

solve(x=subs(x=y, x^2+8*x), y, useassumptions) assuming x::RealRange(-4, Open(infinity));

and my hope was that including the assumption would result in a single solution but it still gives me two solutions as it would without the assumption.

I would like to algorithmically end up with a single solution. Currently I am only working with functions that have variables to the power of 0, 1 or 2 and additionally square roots, but a more general method would be optimal. What am I doing wrong?

Can you use the Dirac function in different coordinate systems?

Dear all

I have a second order PDE, i used pdesolve but no solution obtained, why?

pdsolve_pde.mw

thanks

 

 

Is there a way to ask Maple to re-write the expression 

a:=1/3 -exp(-3)/3 into a:=1/3*(1-exp(-3))  ?

The command "factor" doesn't seem to work. Thank you.


Can the number of frames per second be changed programmatically in animate and/or animatecurve ?

Thanks in advance

I should know this, but I don't: Is there a plotting command to plot a list of points, like so:

list:=[[x1,y1],[x2,y2],etc...]; plotlist(list);

(a Vector of points would also be ok)?

There is plots:-pointplot which plots two Vectors (or maybe lists) against each other.

plots:-listplot plots a list against the index. Both are useful commands I employ a lot, but sometimes I'd like to plot pairs as above directly.

Note that I do know how to transform the list of pairs into two lists, or whatever; that is not the issue. I am looking whether there is a command that does this by itself, transparently, before I program myself such a routine because I am too dense with the Maple Help facility.

Thanks,

Mac Dude.

 

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

 

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

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

 

E.g., rathernt han just showing:

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

 

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

 

 

I have some algebraic expression which I want to expand.

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

Attached below the file with the commands.

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

ExpandSteps.mw
 

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

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

 

NULL


 

Download ExpandSteps.mw

 

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

Hello everyone,

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

 

Thank you so much

Dear maple users,

A fine day wishes to all.

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

Here Psi=0 at x=0

int_c.mw


 

restart:

with(PDEtools):

with(plots):

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

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

(1)

d:=0.5:xi:=0.1:

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

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

(2)

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

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

(3)

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

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

(4)

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

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

(5)

z:=0.98:

NULL

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

[x = proc () option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; evalf(args[1]) end proc, t = proc () option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; evalf(args[2]) end proc, f(x, t) = proc () local tv, xv, solnproc, stype, ndsol, vals; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; Digits := trunc(evalhf(Digits)); solnproc := proc (tv, xv) local INFO, errest, nd, dvars, dary, daryt, daryx, vals, msg, i, j; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; table( [( "soln_procedures" ) = array( 1 .. 1, [( 1 ) = (4374356738)  ] ) ] ) INFO := table( [( "depshift" ) = [1, 2], ( "solmat_v" ) = Vector(462, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0, (102) = .0, (103) = .0, (104) = .0, (105) = .0, (106) = .0, (107) = .0, (108) = .0, (109) = .0, (110) = .0, (111) = .0, (112) = .0, (113) = .0, (114) = .0, (115) = .0, (116) = .0, (117) = .0, (118) = .0, (119) = .0, (120) = .0, (121) = .0, (122) = .0, (123) = .0, (124) = .0, (125) = .0, (126) = .0, (127) = .0, (128) = .0, (129) = .0, (130) = .0, (131) = .0, (132) = .0, (133) = .0, (134) = .0, (135) = .0, (136) = .0, (137) = .0, (138) = .0, (139) = .0, (140) = .0, (141) = .0, (142) = .0, (143) = .0, (144) = .0, (145) = .0, (146) = .0, (147) = .0, (148) = .0, (149) = .0, (150) = .0, (151) = .0, (152) = .0, (153) = .0, (154) = .0, (155) = .0, (156) = .0, (157) = .0, (158) = .0, (159) = .0, (160) = .0, (161) = .0, (162) = .0, (163) = .0, (164) = .0, (165) = .0, (166) = .0, (167) = .0, (168) = .0, (169) = .0, (170) = .0, (171) = .0, (172) = .0, (173) = .0, (174) = .0, (175) = .0, (176) = .0, (177) = .0, (178) = .0, (179) = .0, (180) = .0, (181) = .0, (182) = .0, (183) = .0, (184) = .0, (185) = .0, (186) = .0, (187) = .0, (188) = .0, (189) = .0, (190) = .0, (191) = .0, (192) = .0, (193) = .0, (194) = .0, (195) = .0, (196) = .0, (197) = .0, (198) = .0, (199) = .0, (200) = .0, (201) = .0, (202) = .0, (203) = .0, (204) = .0, (205) = .0, (206) = .0, (207) = .0, (208) = .0, (209) = .0, (210) = .0, (211) = .0, (212) = .0, (213) = .0, (214) = .0, (215) = .0, (216) = .0, (217) = .0, (218) = .0, (219) = .0, (220) = .0, (221) = .0, (222) = .0, (223) = .0, (224) = .0, (225) = .0, (226) = .0, (227) = .0, (228) = .0, (229) = .0, (230) = .0, (231) = .0, (232) = .0, (233) = .0, (234) = .0, (235) = .0, (236) = .0, (237) = .0, (238) = .0, (239) = .0, (240) = .0, (241) = .0, (242) = .0, (243) = .0, (244) = .0, (245) = .0, (246) = .0, (247) = .0, (248) = .0, (249) = .0, (250) = .0, (251) = .0, (252) = .0, (253) = .0, (254) = .0, (255) = .0, (256) = .0, (257) = .0, (258) = .0, (259) = .0, (260) = .0, (261) = .0, (262) = .0, (263) = .0, (264) = .0, (265) = .0, (266) = .0, (267) = .0, (268) = .0, (269) = .0, (270) = .0, (271) = .0, (272) = .0, (273) = .0, (274) = .0, (275) = .0, (276) = .0, (277) = .0, (278) = .0, (279) = .0, (280) = .0, (281) = .0, (282) = .0, (283) = .0, (284) = .0, (285) = .0, (286) = .0, (287) = .0, (288) = .0, (289) = .0, (290) = .0, (291) = .0, (292) = .0, (293) = .0, (294) = .0, (295) = .0, (296) = .0, (297) = .0, (298) = .0, (299) = .0, (300) = .0, (301) = .0, (302) = .0, (303) = .0, (304) = .0, (305) = .0, (306) = .0, (307) = .0, (308) = .0, (309) = .0, (310) = .0, (311) = .0, (312) = .0, (313) = .0, (314) = .0, (315) = .0, (316) = .0, (317) = .0, (318) = .0, (319) = .0, (320) = .0, (321) = .0, (322) = .0, (323) = .0, (324) = .0, (325) = .0, (326) = .0, (327) = .0, (328) = .0, (329) = .0, (330) = .0, (331) = .0, (332) = .0, (333) = .0, (334) = .0, (335) = .0, (336) = .0, (337) = .0, (338) = .0, (339) = .0, (340) = .0, (341) = .0, (342) = .0, (343) = .0, (344) = .0, (345) = .0, (346) = .0, (347) = .0, (348) = .0, (349) = .0, (350) = .0, (351) = .0, (352) = .0, (353) = .0, (354) = .0, (355) = .0, (356) = .0, (357) = .0, (358) = .0, (359) = .0, (360) = .0, (361) = .0, (362) = .0, (363) = .0, (364) = .0, (365) = .0, (366) = .0, (367) = .0, (368) = .0, (369) = .0, (370) = .0, (371) = .0, (372) = .0, (373) = .0, (374) = .0, (375) = .0, (376) = .0, (377) = .0, (378) = .0, (379) = .0, (380) = .0, (381) = .0, (382) = .0, (383) = .0, (384) = .0, (385) = .0, (386) = .0, (387) = .0, (388) = .0, (389) = .0, (390) = .0, (391) = .0, (392) = .0, (393) = .0, (394) = .0, (395) = .0, (396) = .0, (397) = .0, (398) = .0, (399) = .0, (400) = .0, (401) = .0, (402) = .0, (403) = .0, (404) = .0, (405) = .0, (406) = .0, (407) = .0, (408) = .0, (409) = .0, (410) = .0, (411) = .0, (412) = .0, (413) = .0, (414) = .0, (415) = .0, (416) = .0, (417) = .0, (418) = .0, (419) = .0, (420) = .0, (421) = .0, (422) = .0, (423) = .0, (424) = .0, (425) = .0, (426) = .0, (427) = .0, (428) = .0, (429) = .0, (430) = .0, (431) = .0, (432) = .0, (433) = .0, (434) = .0, (435) = .0, (436) = .0, (437) = .0, (438) = .0, (439) = .0, (440) = .0, (441) = .0, (442) = .0, (443) = .0, (444) = .0, (445) = .0, (446) = .0, (447) = .0, (448) = .0, (449) = .0, (450) = .0, (451) = .0, (452) = .0, (453) = .0, (454) = .0, (455) = .0, (456) = .0, (457) = .0, (458) = .0, (459) = .0, (460) = .0, (461) = .0, (462) = .0}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(42, 11, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (13, 9) = .0, (13, 10) = .0, (13, 11) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (14, 9) = .0, (14, 10) = .0, (14, 11) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (15, 9) = .0, (15, 10) = .0, (15, 11) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (16, 9) = .0, (16, 10) = .0, (16, 11) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (17, 9) = .0, (17, 10) = .0, (17, 11) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (18, 9) = .0, (18, 10) = .0, (18, 11) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (19, 9) = .0, (19, 10) = .0, (19, 11) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (20, 9) = .0, (20, 10) = .0, (20, 11) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0, (21, 9) = .0, (21, 10) = .0, (21, 11) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (22, 7) = .0, (22, 8) = .0, (22, 9) = .0, (22, 10) = .0, (22, 11) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (23, 7) = .0, (23, 8) = .0, (23, 9) = .0, (23, 10) = .0, (23, 11) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (24, 7) = .0, (24, 8) = .0, (24, 9) = .0, (24, 10) = .0, (24, 11) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (25, 7) = .0, (25, 8) = .0, (25, 9) = .0, (25, 10) = .0, (25, 11) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (26, 7) = .0, (26, 8) = .0, (26, 9) = .0, (26, 10) = .0, (26, 11) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (27, 7) = .0, (27, 8) = .0, (27, 9) = .0, (27, 10) = .0, (27, 11) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (28, 7) = .0, (28, 8) = .0, (28, 9) = .0, (28, 10) = .0, (28, 11) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (29, 7) = .0, (29, 8) = .0, (29, 9) = .0, (29, 10) = .0, (29, 11) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (30, 7) = .0, (30, 8) = .0, (30, 9) = .0, (30, 10) = .0, (30, 11) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (31, 7) = .0, (31, 8) = .0, (31, 9) = .0, (31, 10) = .0, (31, 11) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (32, 7) = .0, (32, 8) = .0, (32, 9) = .0, (32, 10) = .0, (32, 11) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (33, 7) = .0, (33, 8) = .0, (33, 9) = .0, (33, 10) = .0, (33, 11) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (34, 7) = .0, (34, 8) = .0, (34, 9) = .0, (34, 10) = .0, (34, 11) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (35, 7) = .0, (35, 8) = .0, (35, 9) = .0, (35, 10) = .0, (35, 11) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (36, 7) = .0, (36, 8) = .0, (36, 9) = .0, (36, 10) = .0, (36, 11) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (37, 7) = .0, (37, 8) = .0, (37, 9) = .0, (37, 10) = .0, (37, 11) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (38, 7) = .0, (38, 8) = .0, (38, 9) = .0, (38, 10) = .0, (38, 11) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (39, 7) = .0, (39, 8) = .0, (39, 9) = .0, (39, 10) = .0, (39, 11) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (40, 7) = .0, (40, 8) = .0, (40, 9) = .0, (40, 10) = .0, (40, 11) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (41, 7) = .0, (41, 8) = .0, (41, 9) = .0, (41, 10) = .0, (41, 11) = .0, (42, 1) = .0, (42, 2) = .0, (42, 3) = .0, (42, 4) = .0, (42, 5) = .0, (42, 6) = .0, (42, 7) = .0, (42, 8) = .0, (42, 9) = .0, (42, 10) = .0, (42, 11) = .0}, datatype = float[8], order = C_order))]), ( "initialized" ) = false, ( "indepvars" ) = [x, t], ( "explicit" ) = false, ( "depvars" ) = [f, theta], ( "mixed" ) = false, ( "solvec4" ) = Vector(42, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0}, datatype = float[8]), ( "autonomous" ) = true, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s10, _s11, _s12, _s13, _s2, _s3, _s4, _s5, _s6, _s7, _s8, _s9, xi; _s5 := -2300735754*k; _s6 := -4601471508*k; _s7 := -4000000000*h^2; _s8 := -8000000000*h^2; _s9 := -1150367877*k*h; _s10 := -2000000000*k*h^2; _s11 := -4000000000*k*h^2; _s12 := -_s6-_s7; _s13 := -_s6-_s8; vec[1] := (-(3/2)*v[1]+2*v[3]-(1/2)*v[5])/h; vec[-1+2*n] := v[-1+2*n]; for xi from 2 to n-1 do _s1 := -vp[-3+2*xi]+vp[1+2*xi]; _s4 := vp[-3+2*xi]-2*vp[-1+2*xi]+vp[1+2*xi]; vec[-1+2*xi] := (_s5*_s4*v[2*xi]*x[xi]+_s5*_s4*vp[2*xi]*x[xi]+_s5*v[2*xi]*v[-3+2*xi]*x[xi]-_s6*v[2*xi]*v[-1+2*xi]*x[xi]+_s5*v[2*xi]*v[1+2*xi]*x[xi]+_s5*v[-3+2*xi]*vp[2*xi]*x[xi]-_s6*v[-1+2*xi]*vp[2*xi]*x[xi]+_s5*v[1+2*xi]*vp[2*xi]*x[xi]-_s9*_s1-_s11*x[xi]+_s9*v[-3+2*xi]-_s9*v[1+2*xi]-_s12*v[-1+2*xi]*x[xi]+_s9*_s1*v[2*xi]+_s9*_s1*vp[2*xi]-_s5*_s4*x[xi]-_s9*v[2*xi]*v[-3+2*xi]+_s9*v[2*xi]*v[1+2*xi]-_s9*v[-3+2*xi]*vp[2*xi]+_s9*v[1+2*xi]*vp[2*xi]-_s7*vp[-1+2*xi]*x[xi]-_s10*x[xi]*v[2*xi]-_s10*x[xi]*vp[2*xi]-_s5*v[-3+2*xi]*x[xi]-_s5*v[1+2*xi]*x[xi])/(_s11*x[xi]) end do; vec[2] := (-(3/2)*v[2]+2*v[4]-(1/2)*v[6])/h; vec[2*n] := v[2*n]-1; for xi from 2 to n-1 do _s2 := -vp[2*xi-2]+vp[2+2*xi]; _s3 := vp[2*xi-2]-2*vp[2*xi]+vp[2+2*xi]; vec[2*xi] := -(_s13*v[2*xi]*x[xi]+_s3*_s5*x[xi]+_s5*v[2+2*xi]*x[xi]+_s5*v[2*xi-2]*x[xi]+_s8*vp[2*xi]*x[xi]+_s2*_s9+_s9*v[2+2*xi]-_s9*v[2*xi-2])/(_s11*x[xi]) end do end proc, ( "adjusted" ) = false, ( "solmatrix" ) = Matrix(42, 11, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (1, 9) = .0, (1, 10) = .0, (1, 11) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (2, 9) = .0, (2, 10) = .0, (2, 11) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (3, 9) = .0, (3, 10) = .0, (3, 11) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (4, 9) = .0, (4, 10) = .0, (4, 11) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (5, 9) = .0, (5, 10) = .0, (5, 11) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (6, 9) = .0, (6, 10) = .0, (6, 11) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (7, 9) = .0, (7, 10) = .0, (7, 11) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (8, 9) = .0, (8, 10) = .0, (8, 11) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (9, 9) = .0, (9, 10) = .0, (9, 11) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (10, 9) = .0, (10, 10) = .0, (10, 11) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (11, 9) = .0, (11, 10) = .0, (11, 11) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (12, 9) = .0, (12, 10) = .0, (12, 11) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (13, 9) = .0, (13, 10) = .0, (13, 11) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (14, 9) = .0, (14, 10) = .0, (14, 11) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (15, 9) = .0, (15, 10) = .0, (15, 11) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (16, 9) = .0, (16, 10) = .0, (16, 11) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (17, 9) = .0, (17, 10) = .0, (17, 11) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (18, 9) = .0, (18, 10) = .0, (18, 11) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (19, 9) = .0, (19, 10) = .0, (19, 11) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (20, 9) = .0, (20, 10) = .0, (20, 11) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0, (21, 9) = .0, (21, 10) = .0, (21, 11) = .0, (22, 1) = .0, (22, 2) = .0, (22, 3) = .0, (22, 4) = .0, (22, 5) = .0, (22, 6) = .0, (22, 7) = .0, (22, 8) = .0, (22, 9) = .0, (22, 10) = .0, (22, 11) = .0, (23, 1) = .0, (23, 2) = .0, (23, 3) = .0, (23, 4) = .0, (23, 5) = .0, (23, 6) = .0, (23, 7) = .0, (23, 8) = .0, (23, 9) = .0, (23, 10) = .0, (23, 11) = .0, (24, 1) = .0, (24, 2) = .0, (24, 3) = .0, (24, 4) = .0, (24, 5) = .0, (24, 6) = .0, (24, 7) = .0, (24, 8) = .0, (24, 9) = .0, (24, 10) = .0, (24, 11) = .0, (25, 1) = .0, (25, 2) = .0, (25, 3) = .0, (25, 4) = .0, (25, 5) = .0, (25, 6) = .0, (25, 7) = .0, (25, 8) = .0, (25, 9) = .0, (25, 10) = .0, (25, 11) = .0, (26, 1) = .0, (26, 2) = .0, (26, 3) = .0, (26, 4) = .0, (26, 5) = .0, (26, 6) = .0, (26, 7) = .0, (26, 8) = .0, (26, 9) = .0, (26, 10) = .0, (26, 11) = .0, (27, 1) = .0, (27, 2) = .0, (27, 3) = .0, (27, 4) = .0, (27, 5) = .0, (27, 6) = .0, (27, 7) = .0, (27, 8) = .0, (27, 9) = .0, (27, 10) = .0, (27, 11) = .0, (28, 1) = .0, (28, 2) = .0, (28, 3) = .0, (28, 4) = .0, (28, 5) = .0, (28, 6) = .0, (28, 7) = .0, (28, 8) = .0, (28, 9) = .0, (28, 10) = .0, (28, 11) = .0, (29, 1) = .0, (29, 2) = .0, (29, 3) = .0, (29, 4) = .0, (29, 5) = .0, (29, 6) = .0, (29, 7) = .0, (29, 8) = .0, (29, 9) = .0, (29, 10) = .0, (29, 11) = .0, (30, 1) = .0, (30, 2) = .0, (30, 3) = .0, (30, 4) = .0, (30, 5) = .0, (30, 6) = .0, (30, 7) = .0, (30, 8) = .0, (30, 9) = .0, (30, 10) = .0, (30, 11) = .0, (31, 1) = .0, (31, 2) = .0, (31, 3) = .0, (31, 4) = .0, (31, 5) = .0, (31, 6) = .0, (31, 7) = .0, (31, 8) = .0, (31, 9) = .0, (31, 10) = .0, (31, 11) = .0, (32, 1) = .0, (32, 2) = .0, (32, 3) = .0, (32, 4) = .0, (32, 5) = .0, (32, 6) = .0, (32, 7) = .0, (32, 8) = .0, (32, 9) = .0, (32, 10) = .0, (32, 11) = .0, (33, 1) = .0, (33, 2) = .0, (33, 3) = .0, (33, 4) = .0, (33, 5) = .0, (33, 6) = .0, (33, 7) = .0, (33, 8) = .0, (33, 9) = .0, (33, 10) = .0, (33, 11) = .0, (34, 1) = .0, (34, 2) = .0, (34, 3) = .0, (34, 4) = .0, (34, 5) = .0, (34, 6) = .0, (34, 7) = .0, (34, 8) = .0, (34, 9) = .0, (34, 10) = .0, (34, 11) = .0, (35, 1) = .0, (35, 2) = .0, (35, 3) = .0, (35, 4) = .0, (35, 5) = .0, (35, 6) = .0, (35, 7) = .0, (35, 8) = .0, (35, 9) = .0, (35, 10) = .0, (35, 11) = .0, (36, 1) = .0, (36, 2) = .0, (36, 3) = .0, (36, 4) = .0, (36, 5) = .0, (36, 6) = .0, (36, 7) = .0, (36, 8) = .0, (36, 9) = .0, (36, 10) = .0, (36, 11) = .0, (37, 1) = .0, (37, 2) = .0, (37, 3) = .0, (37, 4) = .0, (37, 5) = .0, (37, 6) = .0, (37, 7) = .0, (37, 8) = .0, (37, 9) = .0, (37, 10) = .0, (37, 11) = .0, (38, 1) = .0, (38, 2) = .0, (38, 3) = .0, (38, 4) = .0, (38, 5) = .0, (38, 6) = .0, (38, 7) = .0, (38, 8) = .0, (38, 9) = .0, (38, 10) = .0, (38, 11) = .0, (39, 1) = .0, (39, 2) = .0, (39, 3) = .0, (39, 4) = .0, (39, 5) = .0, (39, 6) = .0, (39, 7) = .0, (39, 8) = .0, (39, 9) = .0, (39, 10) = .0, (39, 11) = .0, (40, 1) = .0, (40, 2) = .0, (40, 3) = .0, (40, 4) = .0, (40, 5) = .0, (40, 6) = .0, (40, 7) = .0, (40, 8) = .0, (40, 9) = .0, (40, 10) = .0, (40, 11) = .0, (41, 1) = .0, (41, 2) = .0, (41, 3) = .0, (41, 4) = .0, (41, 5) = .0, (41, 6) = .0, (41, 7) = .0, (41, 8) = .0, (41, 9) = .0, (41, 10) = .0, (41, 11) = .0, (42, 1) = .0, (42, 2) = .0, (42, 3) = .0, (42, 4) = .0, (42, 5) = .0, (42, 6) = .0, (42, 7) = .0, (42, 8) = .0, (42, 9) = .0, (42, 10) = .0, (42, 11) = .0}, datatype = float[8], order = C_order), ( "eqndep" ) = [1, 2], ( "timevar" ) = t, ( "intspace" ) = Matrix(21, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0, (8, 1) = .0, (8, 2) = .0, (9, 1) = .0, (9, 2) = .0, (10, 1) = .0, (10, 2) = .0, (11, 1) = .0, (11, 2) = .0, (12, 1) = .0, (12, 2) = .0, (13, 1) = .0, (13, 2) = .0, (14, 1) = .0, (14, 2) = .0, (15, 1) = .0, (15, 2) = .0, (16, 1) = .0, (16, 2) = .0, (17, 1) = .0, (17, 2) = .0, (18, 1) = .0, (18, 2) = .0, (19, 1) = .0, (19, 2) = .0, (20, 1) = .0, (20, 2) = .0, (21, 1) = .0, (21, 2) = .0}, datatype = float[8], order = C_order), ( "solspace" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = 1.0}, datatype = float[8]), ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s10, _s11, _s12, _s13, _s2, _s3, _s4, _s5, _s6, _s7, _s8, _s9, xi; _s3 := -1150367877*h; _s4 := -2300735754*k; _s5 := 4601471508*k; _s6 := 4000000000*h^2; _s7 := -1150367877*k*h; _s8 := 1000000000*k*h^2; _s9 := 2000000000*k*h^2; _s10 := 4000000000*k*h^2; _s11 := (1150367877/1000000000)/h^2; _s12 := -2000000000*h^2-1150367877*k; _s13 := -(1/1000000000)*(1000000000*h^2+1150367877*k)/(k*h^2); mat[4] := (3/2)/h; mat[6] := -2/h; mat[8] := (1/2)/h; mat[22*n-18] := -1; for xi from 2 to n-1 do _s1 := -vp[-3+2*xi]+vp[1+2*xi]; _s2 := vp[-3+2*xi]-2*vp[-1+2*xi]+vp[1+2*xi]; mat[22*xi-17] := (_s2*_s4*x[xi]+_s4*v[-3+2*xi]*x[xi]+_s4*v[1+2*xi]*x[xi]+_s5*v[-1+2*xi]*x[xi]+_s1*_s7-_s7*v[-3+2*xi]+_s7*v[1+2*xi]+_s9*x[xi])/(_s10*x[xi]); mat[22*xi-20] := -(-1+v[2*xi]+vp[2*xi])*(_s3+2300735754*x[xi])/(_s6*x[xi]); mat[22*xi-18] := _s11*v[2*xi]+_s11*vp[2*xi]+_s13; mat[22*xi-16] := (-1+v[2*xi]+vp[2*xi])*(_s3-2300735754*x[xi])/(_s6*x[xi]) end do; mat[15] := (3/2)/h; mat[17] := -2/h; mat[19] := (1/2)/h; mat[-7+22*n] := -1; for xi from 2 to n-1 do mat[-7+22*xi] := _s12/_s8; mat[-5+22*xi] := -(_s4*x[xi]+_s7)/(_s10*x[xi]); mat[-9+22*xi] := -(_s4*x[xi]-_s7)/(_s10*x[xi]) end do end proc, ( "timeidx" ) = 2, ( "totalwidth" ) = 11, ( "spacepts" ) = 21, ( "depeqn" ) = [1, 2], ( "maxords" ) = [2, 1], ( "bandwidth" ) = [2, 6], ( "timestep" ) = 0.500000000000000e-1, ( "minspcpoints" ) = 4, ( "spacevar" ) = x, ( "spacestep" ) = 0.500000000000000e-1, ( "fdepvars" ) = [f(x, t), theta(x, t)], ( "theta" ) = 1/2, ( "spaceadaptive" ) = false, ( "periodic" ) = false, ( "solmat_ne" ) = 0, ( "pts", x ) = [0, 1], ( "solvec5" ) = Vector(42, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0}, datatype = float[8]), ( "extrabcs" ) = [0, 0], ( "solution" ) = Array(1..3, 1..21, 1..2, {(1, 1, 1) = .0, (1, 1, 2) = .0, (1, 2, 1) = .0, (1, 2, 2) = .0, (1, 3, 1) = .0, (1, 3, 2) = .0, (1, 4, 1) = .0, (1, 4, 2) = .0, (1, 5, 1) = .0, (1, 5, 2) = .0, (1, 6, 1) = .0, (1, 6, 2) = .0, (1, 7, 1) = .0, (1, 7, 2) = .0, (1, 8, 1) = .0, (1, 8, 2) = .0, (1, 9, 1) = .0, (1, 9, 2) = .0, (1, 10, 1) = .0, (1, 10, 2) = .0, (1, 11, 1) = .0, (1, 11, 2) = .0, (1, 12, 1) = .0, (1, 12, 2) = .0, (1, 13, 1) = .0, (1, 13, 2) = .0, (1, 14, 1) = .0, (1, 14, 2) = .0, (1, 15, 1) = .0, (1, 15, 2) = .0, (1, 16, 1) = .0, (1, 16, 2) = .0, (1, 17, 1) = .0, (1, 17, 2) = .0, (1, 18, 1) = .0, (1, 18, 2) = .0, (1, 19, 1) = .0, (1, 19, 2) = .0, (1, 20, 1) = .0, (1, 20, 2) = .0, (1, 21, 1) = .0, (1, 21, 2) = .0, (2, 1, 1) = .0, (2, 1, 2) = .0, (2, 2, 1) = .0, (2, 2, 2) = .0, (2, 3, 1) = .0, (2, 3, 2) = .0, (2, 4, 1) = .0, (2, 4, 2) = .0, (2, 5, 1) = .0, (2, 5, 2) = .0, (2, 6, 1) = .0, (2, 6, 2) = .0, (2, 7, 1) = .0, (2, 7, 2) = .0, (2, 8, 1) = .0, (2, 8, 2) = .0, (2, 9, 1) = .0, (2, 9, 2) = .0, (2, 10, 1) = .0, (2, 10, 2) = .0, (2, 11, 1) = .0, (2, 11, 2) = .0, (2, 12, 1) = .0, (2, 12, 2) = .0, (2, 13, 1) = .0, (2, 13, 2) = .0, (2, 14, 1) = .0, (2, 14, 2) = .0, (2, 15, 1) = .0, (2, 15, 2) = .0, (2, 16, 1) = .0, (2, 16, 2) = .0, (2, 17, 1) = .0, (2, 17, 2) = .0, (2, 18, 1) = .0, (2, 18, 2) = .0, (2, 19, 1) = .0, (2, 19, 2) = .0, (2, 20, 1) = .0, (2, 20, 2) = .0, (2, 21, 1) = .0, (2, 21, 2) = .0, (3, 1, 1) = .0, (3, 1, 2) = .0, (3, 2, 1) = .0, (3, 2, 2) = .0, (3, 3, 1) = .0, (3, 3, 2) = .0, (3, 4, 1) = .0, (3, 4, 2) = .0, (3, 5, 1) = .0, (3, 5, 2) = .0, (3, 6, 1) = .0, (3, 6, 2) = .0, (3, 7, 1) = .0, (3, 7, 2) = .0, (3, 8, 1) = .0, (3, 8, 2) = .0, (3, 9, 1) = .0, (3, 9, 2) = .0, (3, 10, 1) = .0, (3, 10, 2) = .0, (3, 11, 1) = .0, (3, 11, 2) = .0, (3, 12, 1) = .0, (3, 12, 2) = .0, (3, 13, 1) = .0, (3, 13, 2) = .0, (3, 14, 1) = .0, (3, 14, 2) = .0, (3, 15, 1) = .0, (3, 15, 2) = .0, (3, 16, 1) = .0, (3, 16, 2) = .0, (3, 17, 1) = .0, (3, 17, 2) = .0, (3, 18, 1) = .0, (3, 18, 2) = .0, (3, 19, 1) = .0, (3, 19, 2) = .0, (3, 20, 1) = .0, (3, 20, 2) = .0, (3, 21, 1) = .0, (3, 21, 2) = .0}, datatype = float[8], order = C_order), ( "spaceidx" ) = 1, ( "method" ) = theta, ( "eqnords" ) = [[2, 1], [2, 1]], ( "stages" ) = 1, ( "inputargs" ) = [[diff(f(x, t), t) = 1+1.150367877*(1-2*theta(x, t))*(diff(diff(f(x, t), x), x)+(diff(f(x, t), x))/x)+theta(x, t), 2*(diff(theta(x, t), t)) = 1.150367877*(diff(diff(theta(x, t), x), x))+1.150367877*(diff(theta(x, t), x))/x], {f(1, t) = 0, f(x, 0) = 0, theta(1, t) = 1, theta(x, 0) = 0, (D[1](f))(0, t) = 0, (D[1](theta))(0, t) = 0}, time = t], ( "timeadaptive" ) = false, ( "startup_only" ) = false, ( "multidep" ) = [false, false], ( "errorest" ) = false, ( "solvec1" ) = Vector(42, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0}, datatype = float[8]), ( "IBC" ) = b, ( "solmat_is" ) = 0, ( "dependson" ) = [{1, 2}, {2}], ( "leftwidth" ) = 1, ( "BCS", 2 ) = {[[2, 0, 1], b[2, 0, 1]-1], [[2, 1, 0], b[2, 1, 0]]}, ( "solvec2" ) = Vector(42, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0}, datatype = float[8]), ( "depdords" ) = [[[2, 1], [0, 0]], [[0, 0], [2, 1]]], ( "erroraccum" ) = true, ( "ICS" ) = [0, 0], ( "BCS", 1 ) = {[[1, 0, 1], b[1, 0, 1]], [[1, 1, 0], b[1, 1, 0]]}, ( "rightwidth" ) = 0, ( "t0" ) = 0, ( "solmat_i1" ) = 0, ( "PDEs" ) = [diff(f(x, t), t)-1-(1150367877/1000000000)*(1-2*theta(x, t))*(diff(diff(f(x, t), x), x)+(diff(f(x, t), x))/x)-theta(x, t), 2*(diff(theta(x, t), t))-(1150367877/1000000000)*(diff(diff(theta(x, t), x), x))-(1150367877/1000000000)*(diff(theta(x, t), x))/x], ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "solvec3" ) = Vector(42, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0}, datatype = float[8]), ( "banded" ) = true, ( "linear" ) = false, ( "matrixhf" ) = true, ( "depords" ) = [[2, 1], [2, 1]], ( "allocspace" ) = 21, ( "norigdepvars" ) = 2, ( "solmat_i2" ) = 0, ( "vectorhf" ) = true ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(4, {(1) = .0, (2) = .0, (3) = .0, (4) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := [proc (t, x, u) u[1] end proc]; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2:
", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2:
", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "2nd"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc]

(6)

t := 1;

1

(7)

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

.8692871388*x*fN(x, 1)

(8)

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

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

(9)

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

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

 

Find_c1:=solve(W11,C1);

"Find_c1:="

(10)

``


 

Download int_c.mw

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

 

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

How is that? Where did i go wrong? 

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

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

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

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

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

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

(1)

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

 

``


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

Greetings,

 

The Function 

Download Discrete_Dynamical_Models_3.mw

 

Worksheet_1.mw

Dear members,

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

 

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

    chi(i)-w(k)=0.

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

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

Below is my code:

 

 

 

The output is

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

 

Thank you and best regards,

Paul

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

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