Journal of Applied Mathematics
Volume 2012 (2012), Article ID 103205, 13 pages
http://dx.doi.org/10.1155/2012/103205
Research Article

A Nonclassical Radau Collocation Method for Nonlinear Initial-Value Problems with Applications to Lane-Emden Type Equations

Mohammad Maleki,1 M. Tavassoli Kajani,2 I. Hashim,1 A. Kilicman,3 and K. A. M. Atan4

1School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia
2Department of Mathematics, Islamic Azad University, Khorasgan Branch, Isfahan 71595, Iran
3Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
4Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 21 March 2012; Revised 16 September 2012; Accepted 16 September 2012

Academic Editor: Igor Andrianov

Copyright © 2012 Mohammad Maleki 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 a numerical method for solving nonlinear initial-value problems of Lane-Emden type. The method is based upon nonclassical Gauss-Radau collocation points, and weighted interpolation. Nonclassical orthogonal polynomials, nonclassical Radau points and weighted interpolation are introduced on arbitrary intervals. Then they are utilized to reduce the computation of nonlinear initial-value problems to a system of nonlinear algebraic equations. We also present the comparison of this work with some well-known results and show that the present solution is very accurate.