Finite difference approximations for a fractional diffusion/anti-diffusion equation

Mathematics – Analysis of PDEs

Scientific paper

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Scientific paper

A class of finite difference schemes for solving a fractional anti-diffusive
equation, recently proposed by Andrew C. Fowler to describe the dynamics of
dunes, is considered. Their linear stability is analyzed using the standard Von
Neumann analysis: stability criteria are found and checked numerically.
Moreover, we investigate the consistency and convergence of these schemes.

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