ANALYTICAL SOLUTION OF THE LINEAR AND NONLINEAR KLEIN-GORDON EQUATIONS

Abstract

In this study, three powerful methods, the VIM, NIM and ADM were applied to find the solution of the linear and nonlinear Klein-Gordon equations. To illustrate the ability and reliability of the methods some examples were provided. In this study, we compare numerical results with the exact solution. The results show that the Variational Iteration Method, Adomian Decomposition Method and New Iterative Method are powerful and effective tools in solving the Klein-Gordon equations and can be used to solve other linear and nonlinear equations, ordinary and partial equations.