Solving the Two–Dimensional Lane–Emden Type Equations by the Adomian Decomposition Method

Abstract

In this paper, we introduce the two–dimensional Lane–Emden type equations. We study the linear and the nonlinear forms of these types of equations. We use the systematic Adomian decomposition method to handle these equations with specified initial conditions. The Adomian decomposition method provides an efficient scheme for exact and approximate analytic solutions of singular nonlinear equations. We corroborate this work by studying several two-dimensional Lane-Emden problems that represent numerical examples to show the strength of our approach.