Dear Friends

I have a problem in CPU time in MAPLE.

I write the codes in maple related to the nonlinear heat conduction problem in one dimension by Collocation method, but after 30 minutes no solution has been observed!!!

My codes are for N=4!, i.e., I have 25 equations with 25 unknowns!!!

If MAPLE can not solve this simple system, How can I solve 3 dimensional pdes by N=9,

In this case, I have 1000 equations with 1000 unknowns!!!

please help me and suggest me a fast iterative solver.

I should remark that my problem is stated in this paper

http://www.sciencedirect.com/science/article/pii/S1018364713000025

If there exist any other suitable method, I will be happy to receive any support.

With kind regards,

Emran Tohidi.

> restart;
> Digits := 20; N := 4; st := time(); u := sum(sum(a[m, n]*x^m*t^n, m = 0 .. N), n = 0 .. N); u := unapply(u, x, t); ut := diff(u(x, t), `$`(t, 1)); ut := unapply(ut, x, t); ku := simplify(1+u(x, t)^2); ku := unapply(ku, x, t); ux := diff(u(x, t), `$`(x, 1)); ux := unapply(ux, x, t); K := ku(x, t)*ux(x, t); K := unapply(K, x, t); Kx := diff(K(x, t), `$`(x, 1)); Kx := unapply(Kx, x, t); f := proc (x, t) options operator, arrow; x*exp(t)*(1-2*exp(2*t)) end proc;
print(`output redirected...`); # input placeholder
> S1 := {seq(u(i/N, 0)-i/N = 0, i = 0 .. N)}; S2 := {seq(u(0, j/N) = 0, j = 1 .. N)}; S3 := {seq(u(1, j/N)+ux(1, j/N)-2*exp(j/N) = 0, j = 1 .. N)}; S4 := {seq(seq(Kx(i/N, j/N)+f(i/N, j/N)-ut(i/N, j/N) = 0, i = 1 .. N-1), j = 1 .. N)}; S := `union`(`union`(`union`(S1, S2), S3), S4); sol := DirectSearch:-SolveEquations([op(S)], tolerances = 10^(-4), evaluationlimit = 1000000);
print(`output redirected...`); # input placeholder
> assign(sol);
%;
> u(x, t);
> CPUTIME := time()-st;
plot3d(u(x, t) - x exp(t), x = 0 .. 1, t = 0 .. 1)

Hello,

I just bought and installed "The mathematical Survival Kit" but I can't figure out how does it work

Anybody can help?

Thanaks

Martina

Pokaż pełną treść

What is the command to get a sequence of the first twenty prime numbers

Code was computed on two different PC:
1) Win 8.1, Maple 17.02 x64
2) Win 8.1, Maple 18.01 x64

In brief:

n:=3: 
Grid:-Seq('f(i)', i = 1 .. n): 

works well in Maple 17.02 but gives an error in Maple 18.01. Why?

However,

(j -> Grid:-Seq('f(i)', i = 1 .. j))(n):

works well for both Maple versions.

according to examples from Maple help page
http://www.maplesoft.com/support/help/Maple/view.aspx?path=Grid%2fSeq
we have to pass exactly 'f(i)' (not just f(i)) into Grid:-Seq(...). Why?

Why doesn't Digits:=30: work properly for Grid:-Seq(...)?

For details see attached file. Output was produced in Maple 17.02. In Maple 18.01 the output will differ.

Download Grid[Seq].mw

i am trying to export an animated gif file but the export windows freezes and exports an empty file with zero bytes

the animation was created by: display(map(p, convert(A(() .. (), 2), list)), insequence = true)

i have tried to give maple some time (2-3 hours) and i even tried to restart the computer and lauch maple and try to export it but it didnt worked

how can i export it or how can i plot the using commands

Greetings everyone. I tried to get the roots of this polynomial by using allvalues command. But I got the roots in indeces instead of the value of the roots.

what should i do?

How to identify whether biased game is changed based on the latest toss from a sequence

can HMM identify this?

for example

if

fair fair fair biased biased fair fair biased

When greek symbols are used in code edit region (by copying from worksheet 2d math mode), they used to get exported properly to PDF but the only issue was large code edit region used to get cut off. But now with this new 18.01 update, code edit region is not cut off but greek symbol inside code edit region are not appearing in PDF export instead just pink boxes. Has anyone else also encountered this issue and suggest a resolution.

how i can trust in DirectSearch solution result.is there any creteria?

my variable is intensity.

this is my code:

ep0 := 1/(4*3.14); el := 8.54*10^(-2); hbar := 1; vf := 1/300; kb := 1; tem := 2.586*10^(-2); ci := 1; p := 1.458*10^16; beta := 2; ai := 7.1*10^(-4); bi := ai/sqrt(3); enph := .196; d := enph/(kb*tem); n0 := 1/(exp(enph/(kb*tem))-1); gama := hbar*vf; intensity := 10000001; w := 1.55; impurity := 7.2*10^3;

g := hbar*beta/(bi^2*sqrt(2*p*enph)); aa := g^2*(n0+1)/(2*Pi*hbar*gama^2); bb := g^2*n0/(2*Pi*hbar*gama^2); cc := 2/(Pi*gama^2); l := (1*hbar)*w/(2*kb*tem);u := el^2*intensity/(32*w*hbar^2);

DirectSearch:-SolveEquations([op([((enph*ln(1+exp(c+enph/(kb*tem)))/(kb*tem)-polylog(2, -exp(c))+polylog(2, -exp(c+enph/(kb*tem))))*enph*(kb*tem)^2-(enph^2*ln(1+exp(c+enph/(kb*tem)))/(kb^2*tem^2)+2*enph*polylog(2, -exp(c+enph/(kb*tem)))/(kb*tem)+2*polylog(3, -exp(c))-2*polylog(3, -exp(c+enph/(kb*tem))))*(kb*tem)^3+(-exp(b)*enph*ln(1+exp(c+enph/(kb*tem)))+exp(c+d)*enph*ln(1+exp(b-d+enph/(kb*tem)))+exp(b)*kb*tem*polylog(2, -exp(c))-exp(c+d)*kb*tem*polylog(2, -exp(b-d))-exp(b)*kb*tem*polylog(2, -exp(c+enph/(kb*tem)))+exp(c+d)*kb*tem*polylog(2, -exp(b-d+enph/(kb*tem))))*enph*(kb*tem)^2/((exp(b)-exp(c+d))*kb*tem)+(exp(b)*enph^2*ln(1+exp(c+enph/(kb*tem)))-exp(c+d)*enph^2*ln(1+exp(b-d+enph/(kb*tem)))+2*exp(b)*enph*kb*tem*polylog(2, -exp(c+enph/(kb*tem)))-2*exp(c+d)*enph*kb*tem*polylog(2, -exp(b-d+enph/(kb*tem)))+2*exp(b)*kb^2*tem^2*polylog(3, -exp(c))-2*exp(c+d)*kb^2*tem^2*polylog(3, -exp(b-d))-2*exp(b)*kb^2*tem^2*polylog(3, -exp(c+enph/(kb*tem)))+2*exp(c+d)*kb^2*tem^2*polylog(3, -exp(b-d+enph/(kb*tem))))*(kb*tem)^3/((exp(b)-exp(c+d))*kb^2*tem^2))*bb+u*(1/(1+exp(-l-c))-1/((1+exp(-l-c))*(1+exp(l-b))))-(((1*enph)*(enph-2*kb*tem*ln(1+exp(-b+enph/(kb*tem))))/(2*kb^2*tem^2)+2*kb^2*tem^2*(-polylog(2, -exp(-b+enph/(kb*tem)))+polylog(2, -cosh(b)+sinh(b))))*enph*(kb*tem)^2-(enph^2*(enph-3*kb*tem*ln(1+exp(-b+enph/(kb*tem))))-6*kb^2*tem^2*(enph*polylog(2, -exp(-b+enph/(kb*tem)))+kb*tem*(-polylog(3, -exp(-b+enph/(kb*tem)))+polylog(3, -cosh(b)+sinh(b)))))*(kb*tem)^3/(3*kb^3*tem^3)-(-exp(b)*enph^2+exp(c+d)*enph^2-2*exp(c+d)*enph*kb*tem*ln(1+exp(-b+enph/(kb*tem)))+2*exp(b)*enph*kb*tem*ln(1+exp(-c-d+enph/(kb*tem)))+2*exp(c+d)*kb^2*tem^2*polylog(2, -exp(-b))-2*exp(b)*kb^2*tem^2*polylog(2, -exp(-c-d))-2*exp(c+d)*kb^2*tem^2*polylog(2, -exp(-b+enph/(kb*tem)))+2*exp(b)*kb^2*tem^2*polylog(2, -exp(-c-d+enph/(kb*tem))))*enph*(kb*tem)^2/((2*(-exp(b)+exp(c+d)))*kb^2*tem^2)-(exp(b)*enph^3-exp(c+d)*enph^3+3*exp(c+d)*enph^2*kb*tem*ln(1+exp(-b+enph/(kb*tem)))-3*exp(b)*enph^2*kb*tem*ln(1+exp(-c-d+enph/(kb*tem)))+6*exp(c+d)*enph*kb^2*tem^2*polylog(2, -exp(-b+enph/(kb*tem)))-6*exp(b)*enph*kb^2*tem^2*polylog(2, -exp(-c-d+enph/(kb*tem)))+6*exp(c+d)*kb^3*tem^3*polylog(3, -exp(-b))-6*exp(b)*kb^3*tem^3*polylog(3, -exp(-c-d))-6*exp(c+d)*kb^3*tem^3*polylog(3, -exp(-b+enph/(kb*tem)))+6*exp(b)*kb^3*tem^3*polylog(3, -exp(-c-d+enph/(kb*tem))))*(kb*tem)^3/((3*(-exp(b)+exp(c+d)))*kb^3*tem^3))*aa-u*(1/(1+exp(l-b))-1/((1+exp(-l-c))*(1+exp(l-b)))) = 0, -cc*polylog(2, -exp(b))+cc*polylog(2, -exp(-c))-impurity = 0])], tolerances = 10^(-8), evaluationlimit = 20000)

Is it within the Physics environment possible to specify two sets, A and B, say, of quantities for which the following holds?

1.) any two elements of A anticommute,

2.) any two elements of B anticommute (as well), but

3.) any quantity from A commutes (not anticommutes) with any quantity from B.

Hello,
I have a system of first order diff. equations which I would like to solve symbolically. Unfortunately, Maple does not solve the system. Do anybody have suggestions how can I solve this system (please see below):

diff(S(t), t) = -eta*(C[max]*w*N-alpha*Q(t))*K(t)*S(t)/(w*N*(S(t)+K(t))),

diff(K(t), t) = S(t)*((z*eta*alpha*(C[max]*w*N-alpha*Q(t))*S(t)-upsilon*(eta*alpha^2*Q(t)^2-2*C[max]*w*N*eta*alpha*Q(t)+((-N*w+z)*alpha+N*C[max]^2*w*eta)*N*w))*K(t)^2+(2*((1/2)*z*eta*(C[max]*w*N-alpha*Q(t))*S(t)+N*w*upsilon*(N*w-z)))*S(t)*alpha*K(t)+N*S(t)^2*w*alpha*upsilon*(N*w-z))/((K(t)^2*alpha*z+3*S(t)*K(t)*alpha*z+S(t)*(2*S(t)*z*alpha+upsilon*(C[max]*w*N-alpha*Q(t))))*(S(t)+K(t))*N*w),

diff(Q(t), t) = (-alpha*z*(z*eta*(C[max]*w*N-alpha*Q(t))*K(t)+N*w*upsilon*(N*w-z))*S(t)^2+(-z^2*eta*alpha*(C[max]*w*N-alpha*Q(t))*K(t)^2-(eta*alpha^2*Q(t)^2-2*C[max]*w*N*eta*alpha*Q(t)+N*w*((2*N*w-2*z)*alpha+N*C[max]^2*w*eta))*z*upsilon*K(t)-N*w*upsilon^2*(N*w-z)*(C[max]*w*N-alpha*Q(t)))*S(t)-N*w*z*alpha*upsilon*K(t)^2*(N*w-z))/((2*S(t)^2*alpha*z+(3*z*alpha*K(t)+upsilon*(C[max]*w*N-alpha*Q(t)))*S(t)+K(t)^2*alpha*z)*N*w*upsilon)

where initials conditions are:

S(0) = S0, K(0) = K0, Q(0) = Q0

Thanks,

Dmitry

Hi Everybody,

I installed the Maple Toolbox for matlab and tried to run my old code.  For some reason, maple('restart') will cause Matlab to lock up.  Any ideas?

Windows 7 64-bit.  Matlab 2012b 32-bit, Maple 18 32-bit

Hi Mapleprimers,

I'm using CodeGeneration to convert a procedure I obtained with unapply() into a Matlab function.  I'm having problems getting the outputting function to run correctly in Matlab.  I'm going to dynamically generating equations, so directly editing the Matlab code won't work here.  I'm having problems getting any output in Matlab.  Here is the code I'm working on:  Series_addGear_codegen.mw

Ideally I would like output in a matrix.  I've tried putting the unapplied procedure in another procedure, but the CodeGeneration doesn't work.

This is the maple output from the function:

unapp(1,2,3,4,5);
{BAT_A = -2.267032891, BAT_V = 271, EM2_A = .4615464218, EM2_P = 125.0790803, EM2_T = -1, EM2_V = 271, EM2_W = 2, GBa_T = 12, GBa_W = 5/3, GBb_T = -4, GBb_W = 5, GEN_A = 1.805486469, GEN_P = 489.2868330, GEN_T = -12, GEN_V = 271, GEN_W = 5/3, ICE_mdot_g = 20}

Since I'll know the order of variables, I want the Matlab function to output:

[-2.267032891,  271,  .4615464218,  125.0790803,  -1, ...]

This is the output after putting the Matlab function in Matlab:

>> unapp(1, 1, 1, 1, 1)
Undefined function or variable 'BAT_A'.

Error in unapp (line 39)
unappreturn = unique([BAT_A == -t35 / 0.271e3 - t73 / 0.271e3 BAT_V == 271 EM2_A == t35 /
0.271e3 EM2_P == t35 EM2_T == -FD_T EM2_V == 271 EM2_W == FD_W GBa_T == t44 GBa_W == t41 GBb_T
== -ICE_T GB

This is the Matlab code that is generated by Maple 18:

MCode:=CodeGeneration[Matlab](unapp, declare = [FD_T::float, FD_W::float, GB_R::float, ICE_T::float, ICE_W::float],defaulttype=float,optimize,defaulttype = numeric);
Warning, could not preprocess. Found `abs` or similar in the 'While'/'For' conditions.
Warning, procedure/module options ignored
function unappreturn = unapp(FD_T, FD_W, GB_R, ICE_T, ICE_W)
t2 = 0.1e1 * FD_T * FD_W;
t5 = abs(FD_W);
t7 = abs(FD_T);
t9 = t5 ^ 2;
t13 = t7 ^ 2;
t15 = t9 * t5;
t21 = t13 * t7;
t23 = t9 ^ 2;
t31 = t13 ^ 2;
t33 = 0.1483000000e3 - 0.4267000000e1 * t5 - 0.1277000000e2 * t7 + 0.3640000000e-1 * t9 - 0.1160000000e1 * t5 * t7 + 0.2580000000e0 * t13 - 0.1181000000e-3 * t15 + 0.5994000000e-3 * t9 * t7 - 0.1171000000e-3 * t5 * t13 - 0.1739000000e-2 * t21 + 0.1245000000e-6 * t23 - 0.1200000000e-5 * t15 * t7 + 0.1584000000e-5 * t9 * t13 - 0.4383000000e-6 * t5 * t21 + 0.2947000000e-5 * t31;
if (-t2 == 0.0e0)
t35 = 0.0e0;
elseif (-t2 < 0.0e0)
t35 = t33;
else
t35 = -t33;
end
t36 = ICE_T * ICE_W;
t37 = 0.1e1 * t36;
t41 = ICE_W / GB_R;
t42 = abs(t41);
t44 = ICE_T * GB_R;
t45 = abs(t44);
t47 = t42 ^ 2;
t51 = t45 ^ 2;
t53 = t47 * t42;
t59 = t51 * t45;
t61 = t47 ^ 2;
t69 = t51 ^ 2;
t71 = 0.5280000000e-11 - 0.3849000000e-13 * t42 + 0.7190000000e2 * t45 + 0.1168000000e-15 * t47 - 0.1296000000e1 * t42 * t45 - 0.2489000000e1 * t51 - 0.1451000000e-18 * t53 - 0.1326000000e-3 * t47 * t45 + 0.8141000000e-2 * t42 * t51 + 0.4539000000e-2 * t59 + 0.6325000000e-22 * t61 + 0.2091000000e-6 * t53 * t45 - 0.3455000000e-5 * t47 * t51 - 0.2499000000e-4 * t42 * t59 + 0.5321000000e-4 * t69;
if (-t37 == 0.0e0)
t73 = 0.0e0;
elseif (-t37 < 0.0e0)
t73 = t71;
else
t73 = -t71;
end
unappreturn = unique([BAT_A == -t35 / 0.271e3 - t73 / 0.271e3 BAT_V == 271 EM2_A == t35 / 0.271e3 EM2_P == t35 EM2_T == -FD_T EM2_V == 271 EM2_W == FD_W GBa_T == t44 GBa_W == t41 GBb_T == -ICE_T GBb_W == ICE_W GEN_A == t73 / 0.271e3 GEN_P == t73 GEN_T == -t44 GEN_V == 271 GEN_W == t41 ICE_mdot_g == t36]);

I am not able to simplify my equation, any help would be appreciated ! I want the  term to be eliminated

Download 1.mw