Question: A problem has been occured in fsolve command

Dear All

I have a question about applying fsolve in MAPLE.

These codes come from an applicable model from heat transfer.

I previously solve such systems, but the fsolve takes long time, for example for N=2, I have 12 equations with 12 unknowns. But the fsolve does not work!

I try by N=3 or N=4, but a similar result has been obtained.

If kindly is possible, please give me a help for using fsolve more efficiently that solve my problem.

I have MAPLE 13 in my PC.

With kind regards,

Emran Tohidi.

> restart;
> with(orthopoly);
print(`output redirected...`); # input placeholder
> Digits := 20;
> N := 3; f := proc (x) options operator, arrow; cos(Pi*(x-1/2)) end proc; h1 := proc (t) options operator, arrow; 0 end proc; h2 := proc (t) options operator, arrow; 0 end proc; E := proc (t) options operator, arrow; cos(.2*Pi)*exp(-t^2) end proc;
print(`output redirected...`); # input placeholder
> u := sum(sum(b[m, n]*P(m, 2*x-1)*P(n, 2*t-1), m = 0 .. N), n = 0 .. N);
print(`output redirected...`); # input placeholder
> u := unapply(u, x, t);
print(`output redirected...`); # input placeholder
> ut := diff(u(x, t), `$`(t, 1)); ut := unapply(ut, x, t);
print(`output redirected...`); # input placeholder
> uxx := diff(u(x, t), `$`(x, 2)); uxx := unapply(uxx, x, t);
print(`output redirected...`); # input placeholder
> a := sum(c[m]*P(m, 2*t-1), m = 0 .. N); a := unapply(a, t);
print(`output redirected...`); # input placeholder
> A := fsolve(P(N+1, 2*x-1) = 0);
print(`output redirected...`); # input placeholder
> S1 := {seq(seq(ut(A[i], A[j])-a(A[j])*uxx(A[i], A[j]) = 0, i = 2 .. N), j = 2 .. N+1)}; S2 := {seq(u(A[i], 0)-f(A[i]) = 0, i = 2 .. N)}; S3 := {seq(u(0, A[j])-h1(A[j]) = 0, j = 1 .. N+1)}; S4 := {seq(u(1, A[j])-h2(A[j]) = 0, j = 1 .. N+1)}; S5 := {seq(u(.3, A[j])-E(A[j]) = 0, j = 1 .. N+1)}; S := `union`(`union`(`union`(`union`(S1, S2), S3), S4), S5);
print(`output redirected...`); # input placeholder
> sol := fsolve(S);