A Semi-Analytic method for Solving Nonlinear Partial Differential Equations

Abstract

In this article, Adomian’s decomposition method is used to give an analytical solution to homogeneous partial differential equations modeling problems in sciences and engineering. The solution algorithm yields a rapidly convergent sequence of analytic approximants, which is readily computable, without recourse to linearization, perturbation and discretization as practiced by the traditional methods. The method provides direct scheme for solving the problems and is capable of greatly reducing the size of computational work while still maintaining high accuracy when compared with the theoretical solution. The method can also help to overcome the problems caused by the shortage of analytical methods for the computation of solutions to nonlinear differential equations.

Keywords: Adomian’s decomposition method, Nonlinear differential equations, Adomian’s polynomials, Polynomial approximations,