Splitting methods for the nonlocal Fowler equation

Afaf Bouharguane (1) , Rémi Carles (2)

1 EDP - Equations aux Dérivées Partielles
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier

We consider a nonlocal scalar conservation law proposed by Andrew C. Fowler to describe the dynamics of dunes, and we develop a numerical procedure based on splitting methods to approximate its solutions. We begin by proving the convergence of the well-known Lie formula, which is an approximation of the exact solution of order one in time. We next use the split-step Fourier method to approximate the continuous problem using the fast Fourier transform and the finite difference method. Our numerical experiments confirm the theoretical results.

Mots clés: Nonlocal operator; Numerical time integration; Operator splitting; Split-step Fourier method; Stability; Error analysis

Domaines: Analyse numérique [math.NA]

Afaf Bouharguane, Rémi Carles. Splitting methods for the nonlocal Fowler equation. Mathematics of Computation, 2014, 83 (287), pp.1121-1141. ⟨10.1090/S0025-5718-2013-02757-3⟩. ⟨hal-00623620v2⟩