A New Approximate Analytical Solution of Kuramoto –Sivashinsky Equation Using Homotopy Analysis Method

Abstract

In this paper, Homotopy Analysis Method (HAM) is applied to obtain approximate analytical solution of modified Kuramoto-Sivashinsky (KS) equation. HAM provides a simple way to adjust and control the convergence region of the series so- lution by introducing several parameters, namely, the auxiliary parameter, h, the auxiliary function, H(x;t), the initial guess, u0(x;t) and the auxiliary linear operator, L; as stated in (1). The obtained results show that HAM yields approximate analytical solutions which are quite close to the exact solution of KS equation, which proves the strength of HAM.