An Implementation Of Laplace Decomposition Method For Constructing Exact Solutions Of Nonlinear Partial Differential Equations

Abstract

The majority of real-world issues are formulated using nonlinear PDEs, which are difficult to solve. Thus, it is required to improve mathematical approaches for solving nonlinear PDEs. The Laplace Transform Method is an effective methodology for solving linear PDEs; however, it is not applicable to nonlinear PDEs. The Adomain decomposition method is used for solving both linear and nonlinear PDEs. In this paper exact solutions of nonlinear PDEs are obtained by combining Laplace transform method together with Adomain decomposition method known as Laplace decomposition method (LDM). This is an excellent mathematical tool which can be used directly to all type of ordinary, partial, fractional and integrodifferential equations without unnecessary assumptions, restrictions, linearization or perturbations which may change the physical behavior of the problem. For nonlinear terms Adomain polynomial are obtained. It is observed that in most of cases the series solution converges to exact functions otherwise its few terms provide high degree of accuracy as compared to numerical solutions.