Journal of Applied Mathematics
Volume 2013 (2013), Article ID 547502, 6 pages
http://dx.doi.org/10.1155/2013/547502
Research Article

Approximate Solutions of Singular Two-Point BVPs Using Legendre Operational Matrix of Differentiation

A. Sami Bataineh,1 A. K. Alomari,2 and I. Hashim3

1Department of Mathematics, Faculty of Science, Al-Balqa' Applied University, Al Salt 19117, Jordan
2Department of Mathematics, Faculty of Science, Hashemite University, Zarqa 13115, Jordan
3School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

Received 22 January 2013; Accepted 17 March 2013

Academic Editor: Sazzad Chowdhury

Copyright © 2013 A. Sami Bataineh 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

Exact and approximate analytical solutions of linear and nonlinear singular two-point boundary value problems (BVPs) are obtained for the first time by the Legendre operational matrix of differentiation. Different from other numerical techniques, shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The accuracy of the technique is demonstrated through several linear and nonlinear test examples.