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Direct versus iterative methods for forward-backward diffusion equations. Numerical comparisons. (English) Zbl 1476.65181

Summary: By far, the standard implementation of finite difference schemes for forward-backward partial differential equations consists in employing an iterative method. This paper collects a series of numerical results which demonstrate that a direct implementation can reduce the computing time. An effective way of choosing the seed for the iterative method naturally arises.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K65 Degenerate parabolic equations
35Q84 Fokker-Planck equations
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
78A35 Motion of charged particles
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