Backward Euler diffusion stability on a finite Dirichlet interval
= Backward Euler diffusion stability on a finite Dirichlet interval
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On $J$ interior Dirichlet grid points, backward Euler diffusion is stable for $\mu\geq0$ and also for the nonphysical branch $\mu\leq-[2\sin^2(\pi/(2(J+1)))]^{-1}$. The latter makes every amplification denominator at most $-1$.