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Equation Solving Wolfram Language Numerical Computation

Question about grid refinement

David C

Posted 3 years ago

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!

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!

POSTED BY: David C