Svein Linge coauthored a text on finite difference methods with Hans Petter Langtangen. The book links mathematical discretization with implementations for partial differential equations, including diffusion equations. Deriving an update formula alongside its stability conditions explains why a physically smoothing equation can nevertheless produce an unstable numerical calculation if the time step is too large.[ref]
Finite Difference Computing with PDEs by Hans Petter Langtangen and Svein Linge. Chapter 3, Section 3.1
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