NUMERICAL ANALYSIS OF THE LINEAR AND NONLINEAR KURAMOTO-SIVASHINSKY EQUATION BY USING DIFFERENTIAL TRANSFORMATION METHOD B. Soltanalizadeh 1 and M. Zarebnia 2 1 Department of Mathematics, Sarab Branch, Islamic Azad University, Sarab, Iran Email: babak.soltanalizadeh@gmail.com 2 Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran Email: zarebnia@uma.ac.ir Received 16 July 2010; accepted 14 January 2011 ABSTRACT In this article, the Differential Transformation method (DTM) has been utilized for finding the exact solution of the Kuramoto-Sivashinsky equation. Exact solutions can be achieved by the known forms of the series solutions. In the end, some numerical tests are presented to demonstrate the effectiveness and efficiency of the proposed method. The results prove that the DTM is one of the powerful techniques for linear and nonlinear equations. Keywords: Kuramoto-Sivashinskyequation, Differential Transformation method, Spectral meth- ods. 1 INTRODUCTION The K-S equation was derived by Kuramoto (Kuramoto 1978) and Sivashinsky (Sivashinsky 1980) independently. It also arises in a variety of applications among which are the modeling of reaction-diffusion systems, flame propagation, and viscous flow problems. Moreover, the K-S equation is also considered to be a prototype of a system with ”self-generated” chaos and the large class of generalized Burgers’ equations. During recent years many authors has been focused on solving this equation numerically and analytically. For example, a finite difference scheme (Akrivis 1992), a finite element Galerkin method (Akrivis 1994), Chebyshev spectral collocation methods (Khater and Temsah 2008), a second-order splitting method (Manickam et al. ) have been presented for solving K-S equation. In (Biswas and Swanson 2007) and (Lopez-Marcos 1994), the analytic of K-S equation considered. In this paper, we use the DTM for numerical study of the linear Kuramoto-Sivashinsky (K-S) equation ∂u ∂t + ∂u ∂x + ∂ 2 u ∂x 2 + ν ∂ 4 u ∂x 4 =0 (1) and nonlinear Kuramoto-Sivashinsky (K-S) equation ∂u ∂t + u ∂u ∂x + ∂ 2 u ∂x 2 + ν ∂ 4 u ∂x 4 =0 (2) Int. J. of Appl. Math. and Mech. 7(12): 63-72, 2011.