Application of Homotopy Perturbation Transform Method for Solving Linear and Nonlinear Klein-Gordon Equations

Abstract

In this paper, the homotopy perturbation transform method (HPTM) has been applied to obtain the solution of the linear and nonlinear Klein-Gordon equations. The homotopy perturbation transform method is a combined form of the Laplace transform method with the homotopy perturbation method. This scheme finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that this technique solves nonlinear problems without using Adomian\u2019s polynomials can be considered as a clear advantage of this technique over the decomposition method. The results reveal that the proposed algorithm is very efficient, simple and can be applied to other nonlinear problems. Mathematics Subject Classification: 35C05, 35C10.