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I am solving a non-linear second order system of PDEs in two variables. The equations are too complicated to write out here, but an essential feature is that there is a propagating wave which then bounces on a boundary.

The problem I have is that the numerics breaks down at the boundary, when the wave reaches this point. I have tried by "trial and error" to just change the way I compute derivatives at this point, but with no luck (I am using finite differences; pseudospectral methods do not work), and I have no idea on how to systematically try to improve the stability and I have no intuition of what can work and what will not work.

Does anyone have any tips on what to try when one encounters such problems? How can I systematically move forward to try to make my numerical scheme stable at the boundary?

edit: Basically, if someone just has a list of ideas to blindly try, that would also be great.

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  • $\begingroup$ A better site for this question is Computational Science. $\endgroup$ – user147263 Apr 30 '15 at 1:08
  • $\begingroup$ Ah ok, did not know about that, thanks. $\endgroup$ – Jonathan Lindgren Apr 30 '15 at 9:59

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