New answers tagged difference-equations
2
So, I've managed to solve this issue, it's mainly due to my malformed input which cause Mathematica stuck. I leave it here for anyone who have the similar issue.
Below is the minimal reproducible test case(still tediously long). You'll found there is a minor difference(there is an empty superscript after a[[i]]) but not visually noticeable, and my InputForm ...
3
First, I would like to make two notes.
This equation has also another very famous name: the time-dependent Ginzburg-Landau equation. As such, it was studied in a huge number of contexts.
The parameter eps should be removed from the very beginning by rescaling x->Sqrt(eps) x; y->Sqrt(eps) y. After that, we come to the following equation:
eq = D[u[t, ...
3
NDSolve
First, the NDSolveValue solution which appeared in the comments above to compare with (edit: added MinPoints->35 per @xzczd's suggestion):
ϵ = 0.001;
eq = D[u[t, x, y], t] == ϵ Laplacian[u[t, x, y], {x, y}] + u[t, x, y] - u[t, x, y]^3;
bc1P = u[t, x, -1] == u[t, x, 1];
bc2P =u[t, -1, y] == u[t, 1, y];
ic = u[0, x, y] == Sin[2 Pi x] + 0.001 Cos[...
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