Finite difference schemes for a Burgers type equation with fractional anti-diffusion

摘要

We investigate finite differences discretizations of a nonlinear nonlocal equation recently introduced by A. C. Fowler to study the morphodynamics of river dunes. Due to the fractional anti-diffusive term, numerical stability must depend on the frequency range of the perturbation. We give sufficient stability criteria of fractional CFL type and show evidence of numerical convergence.