Hi there! I'm new, so apologies if this is the wrong place to post this. I can't seem to improve the grid refinement when solving the following equation.
A = 8;
rmax = 20;
ti = 0;
tf = 80;
\[Omega] = 1/2;
\[Theta]fn =
NDSolveValue[{Derivative[0, 2][\[Theta]][r, t] -
Derivative[2, 0][\[Theta]][r, t] + \[Theta][r, t] +
NeumannValue[Derivative[0, 1][\[Theta]][r, t], r == rmax] ==
0, \[Theta][0, t] == 0, \[Theta][r, ti] == 0,
Derivative[0, 1][\[Theta]][r, ti] ==
r A Sech[r \[Omega]]}, \[Theta], {r, 0, rmax}, {t, ti, tf}];
Manipulate[
Plot[\[Theta]fn[r, t]/r, {r, 0, 20}, PlotRange -> {-1, 1}], {t, 0,
tf}]
Even if I use the option "MaxStepSize->0.001", the result is not improved. I suspect I'm missing something obvious, but any help is greatly appreciated!