An efficient approach to the Klein-Gordon equation: an application of the decomposition method

Abstract

In this paper, we study a reliable numerical approximation of the linear and non-linear Klein-Gordon equations by using the Adomian’s decomposition method. The solution is calculated in the form of a series with easily computable components. We prove the convergence of this method applied to the non-linear Klein-Gordon equation. The numerical results demonstrate the effectiveness of the method for these types of equations. © 2006 Inderscience Enterprises Ltd.