New answers tagged advection
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Some remarks about the code, perhaps cleaning these up already solves the question, especially the initialization error:
Floating point errors are a thing, so if you want to get the expected results, give some wiggle room (0.01 is arbitrary, I would not expect defects above 1e-12 in this place)
N = int((x1 - x0) / h + 0.01)
M = int((t1 - t0) / tau + 0.01)...
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