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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 378593, 10 pages
http://dx.doi.org/10.1155/2013/378593
Research Article

A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method

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

Received 10 April 2013; Accepted 31 May 2013

Academic Editor: Massimo Furi

Copyright © 2013 Omar Abu Arqub 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

A new analytic method is applied to singular initial-value Lane-Emden-type problems, and the effectiveness and performance of the method is studied. The proposed method obtains a Taylor expansion of the solution, and when the solution is polynomial, our method reproduces the exact solution. It is observed that the method is easy to implement, valuable for handling singular phenomena, yields excellent results at a minimum computational cost, and requires less time. Computational results of several test problems are presented to demonstrate the viability and practical usefulness of the method. The results reveal that the method is very effective, straightforward, and simple.