A numerical comparison of a Kawahara equation

Abstract

In this Letter we present an Adomian's decomposition Method (shortly ADM) and the Sinc-Galerkin Method (shortly SGM) for numerical approximation travelling wave solutions of the Kawahara equation. We obtain the exact travelling wave solutions of the Kawahara equation for the initial conditions by using ADM. Then ADM yields the analytic approximate solution with fast convergence rate and high accuracy through previous works. The numerical solutions are compared with the known analytical solutions. (C) 2006 Elsevier B.V. All rights reserved.