Two-step modified natural decomposition method for nonlinear Klein-Gordon equations

Abstract

In the present paper, we propose a two-step modied Natural decom- position method to determine the approximate exact solutions for the nonlinear Klein-Gordon equations. The method is based upon coupling
the modied version of the Adomian decomposition method by Wazwaz and the Natural transform. Amazingly, the proposed method gives exact solutions only in two iterations for the nonlinear Klein-Gordon equations
with quadratic nonlinearity considered as test problems.