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Paper detail

Splitting methods for the nonlocal Fowler equation

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.

preprint2012arXivOpen access
Afaf BouharguaneRemi Carles
math.NA
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Afaf BouharguaneRemi Carles

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