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4. SOLVABILITY OF LINEAR AND NONLINEAR KLEIN-GORDON EQUATION BY VARIATIONAL ITERATION METHOD, NEW ITERATIVE METHOD AND ADOMIAN DECOMPOSITION METHOD by Usman M.A, Shittu M.T. and Solanke O.O.
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SOLVABILITY OF LINEAR AND NONLINEAR KLEIN-GORDON EQUATION BY VARIATIONAL ITERATION METHOD, NEW ITERATIVE METHOD AND ADOMIAN DECOMPOSITION METHOD

Usman M.A., Shittu M.T. and Solanke O.O.

Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoaye, Nigeria

Abstract

In this study, Variational Iteration Method (VIM) developed by Ji-Huan He, Adomian Decomposition Method (ADM) by Adomian, New Iterative Method (NIM) developed by Daftardar Gejji and Jafari and the modified Adomian Decomposition method by Wazwaz have been employed to solve the linear and nonlinear Klein-Gordon equations. The solution is calculated is calculated in the form of series in which its component are computed by applying a recursive relation. To illustrate the ability and reliability of the method some examples are 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 tolls in solving the Klein-Gordon equation and they can be used to solve other linear and nonlinear equations

Keywords:Klein-Gordon equation, Variational iteration Method, Lagrange multiplier, New Iterative Method, Relativistic Wave Equation.

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