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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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