Solving a Class of Singular Two-Point Boundary Value Problems Using New Modified Decomposition Method

Abstract

We introduce an effective methodology for solving a class of linear as well as nonlinear singular two-point boundary value problems. This methodology is based on a modification of Adomian decomposition method (ADM) and a new two fold integral operator. We use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components of solution. Thus, we develop modified recursive scheme without any undetermined coefficients while computing the successive solution components. This modification also avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. However, most of earlier recursive schemes using ADM do require computation of undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the present technique. The results reveal that the method is very effective, straightforward, and simple.