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The controversial stability analysis. (English) Zbl 1032.65103

Summary: We present different techniques for obtaining stability limits for a finite difference scheme – the forward-time and space-centered numerical scheme applied to the convection–diffusion equation. A survey of past attempts to state stability conditions for this scheme illustrates the difficulties in stability analysis that arise as soon as a scheme becomes more complex and illuminates the concepts of necessary and sufficient conditions for stability.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65-03 History of numerical analysis
35K15 Initial value problems for second-order parabolic equations
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