Splitting methods for the nonlocal Fowler equation
Numerical Analysis
2012-08-10 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1109.3275,
title = {Splitting methods for the nonlocal Fowler equation},
author = {Afaf Bouharguane and Remi Carles},
journal= {arXiv preprint arXiv:1109.3275},
year = {2012}
}
Comments
20 pages, 3 figures. Presentation modified, some errors fixed