ANALYTICAL SOLUTION OF THE RELATIVISTIC KLEIN-GORDON WAVE EQUATION

Abstract

In this study, the solution to Klein-Gordon equations with focus on analytical methods is discussed. The analytical methods used in this research are the Variational Iteration Method (VIM) developed by Ji-Huan He, Adomian Decomposition Method (ADM) by Adomian and New Iterative Method (NIM) developed by Daftardar Gejji and Jafari. The modified Adomian Decomposition method by Wazwaz was used to solve the linear inhomogeneous and nonlinear Klein-Gordon equations to accelerate the convergence of the solution and minimizes the size of calculation while still maintaining high accuracy of the analytical solution. All the problems considered yield the exact solutions with few iterations. The solutions obtained were compared with the exact solution and the solutions obtained by other existing methods. The solutions obtained by the three methods yield the same results and all the problems considered show that the Variational Iteration Method, Adomian Decomposition Method and New Iterative Method are very powerful and potent in solving Klein-Gordon equations and can be used to obtain closed form solutions of linear and nonlinear differential equations (ordinary and partial).