Solutions of Klein-Gordon Equation by the Laplace Decomposition Method and Modified Laplace Decomposition Method
R. M. Wayal *
Department of Mathematics, Hutatma Rajguru Mahavidyalaya, Rajgurunagar-410 505, Maharashtra, India.
*Author to whom correspondence should be addressed.
Abstract
In this article, the Laplace decomposition method and Modified Laplace decomposition method have been employed to obtain the exact and approximate solutions of the Klein-Gordon equation with the initial profile. An approximate solution obtained by these methods is in good agreement with the exact solution and shows that these approaches can solve linear and nonlinear problems very effectively and are capable to reduce the size of computational work.
Keywords: Laplace decomposition method, Modified Laplace decomposition method, Klein-Gordon equation, Adomian polynomials, partial differential equations