WAVELETS APPROACHES TO BURGER’S EQUATION

Yacine Benhadid (Saudi Arabia)

Received January 24, 2009

Abstract

We present numerical approaches to Burger’s equation based on standard Galerkin techniques and wavelet functions. The orthonormal wavelet basis is found to stably represent the solution for small viscosity. The oscillations at a shock associated with Gibbs phenomena are, in comparison with finite difference and spectral approximations, reduced and confined to the vicinity of the shock. Numerical results and comparison with classical algorithms are provided.

Keywords and phrases: wavelets, Burger’s equation, Galerkin’s algorithm.