I was trying to plot the following:
j = 10;
a = 0; b = 0; s = 0;
B[n_] = Integrate[2*Sin[n*Pi*x]*x, {x, 0, 1}];
u[x_, t_] = Sum[B[n]*Sin[n*Pi*x]*Exp[-(n*Pi)^2*t], {n, 1, j}];
K[x_, t_] = (1/(2*Pi))*
Integrate[
Exp[I*x*psi]*(Exp[-I*b*psi]*Exp[-I*a*psi^2]*
Exp[-I*t*psi^2])/((1 + psi^2)^s), {psi, -10, 10}];
S = (Total[u[x, t]]/Length[u[x, t]]);
T[x_, t_] = Integrate[K[x - y, t]*y*S, {y, -10, 10}]
Plot3D[T[x, t], {x, 0, 1}, {t, 0.01, 1}, AxesLabel -> {"x", "t", "y"}, Boxed -> False, Mesh -> False]
The problem is that this is a really complicated solution and I would like to get the results numerically, but it ran for a long time and nothing plotted -- just empty axis. In my definition of all the variables -- I have also used the := statement, but it didn't help!
If anyone can please help me with this then I'll greatly appreciate it.
Thanks!
T[x,t]
is a real number ? $\endgroup$