Table of Contents
ISRN Computational Mathematics
Volume 2013, Article ID 262863, 11 pages
http://dx.doi.org/10.1155/2013/262863
Research Article

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

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

Received 10 November 2012; Accepted 5 January 2013

Academic Editors: T. Allahviranloo, L. S. Heath, E. Weber, and J. G. Zhou

Copyright © 2013 Randhir Singh and Jitendra Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.