Journal of Applied Mathematics
Volume 2013 (2013), Article ID 850170, 9 pages
Research Article

A New Tau Method for Solving Nonlinear Lane-Emden Type Equations via Bernoulli Operational Matrix of Differentiation

1Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, Iran
2Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
3Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 18 February 2013; Accepted 24 April 2013

Academic Editor: Mehmet Sezer

Copyright © 2013 E. Tohidi 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.


A new and efficient numerical approach is developed for solving nonlinear Lane-Emden type equations via Bernoulli operational matrix of differentiation. The fundamental structure of the presented method is based on the Tau method together with the Bernoulli polynomial approximations in which a new operational matrix is introduced. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. Also, under several mild conditions the error analysis of the proposed method is provided. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. All calculations are done in Maple 13.