HOMOTOPY PERTURBATION AND ABOODH TRANSFORM FOR SOLVING SINE-GORDEN AND KLEIN-GORDEN EQUATIONS

In this paper, we practiced relatively new, analytical method known as the homotopy perturbation method (HPM) and Aboodh transform is employed to obtain the approximate analytical solution of the Klein–Gordon and sine-Gordon equations. The nonlinear terms can be handled by the use of homotopy perturbation method. The proposed homotopy perturbation method is applied to reformulate the first and the second order initial value problems which leads to the solution in terms of transformed variable, and the series solution that can be obtained by making use of the inverse transformation.