A new approximate analytical solution of kuramoto-Sivashinsky equation using homotopy analysis method

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 solution 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.