Splitting methods for the nonlocal Fowler equation

Details Splitting methods for the nonlocal Fowler equation Splitting methods for the nonlocal Fowler equation

2011-09-15

arxiv.org/abs/1109.3275v1

Mathematics

Numerical Analysis

18 pages, 2 figures

Scientific paper

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.

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