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

Pascal Azerad (1) , Afaf Bouharguane (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier

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.

Mots clés: Error analysis; Anti-diffusive fractional operator; Finite difference approximations; Von Neumann stability analysis; Error analysis.

Domaines: Equations aux dérivées partielles [math.AP]

Pascal Azerad, Afaf Bouharguane. Finite difference approximations for a fractional diffusion/anti-diffusion equation. 2011. ⟨hal-00588323⟩