About this Journal Submit a Manuscript Table of Contents
Advances in Numerical Analysis
Volume 2012 (2012), Article ID 541083, 22 pages
http://dx.doi.org/10.1155/2012/541083
Research Article

New Approach for Solving a Class of Doubly Singular Two-Point Boundary Value Problems Using Adomian Decomposition Method

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

Received 13 October 2012; Revised 3 December 2012; Accepted 5 December 2012

Academic Editor: Norbert Heuer

Copyright © 2012 Randhir Singh et al. 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 propose two new modified recursive schemes for solving a class of doubly singular two-point boundary value problems. These schemes are based on Adomian decomposition method (ADM) and new proposed integral operators. We use all the boundary conditions to derive an integral equation before establishing the recursive schemes for the solution components. Thus we develop recursive schemes without any undetermined coefficients while computing successive solution components, whereas several previous recursive schemes have done so. This modification also avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients with multiple roots, which is required to complete calculation of the solution by several earlier modified recursion schemes using the ADM. The approximate solution is computed in the form of series with easily calculable components. The effectiveness of the proposed approach is tested by considering four examples and results are compared with previous known results.