Consider the following scheme for the diffusion
Chapter 8, Problem 13(choose chapter or problem)
Consider the following scheme for the diffusion equation:un+1 j un1 j 2t =un j+1 +un j1 un+1 j un1 j (x)2 . It uses a centered difference for ut and a modied form of the centered difference for uxx. (a) Solve it for un+1 j in terms of s and the previous time steps. (b) Show that it is stable for all s.
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