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Mathematical Problems in Engineering
Volume 2013, Article ID 423797, 9 pages
http://dx.doi.org/10.1155/2013/423797
Research Article

Bernstein Series Solution of a Class of Lane-Emden Type Equations

1Elementary Mathematics Education Program, Faculty of Education, Mugla Sitki Kocman University, 48000 Mugla, Turkey
2Department of Mathematics, Faculty of Sciences and Arts, Manisa Celal Bayar University, 45000 Manisa, Turkey

Received 17 December 2012; Accepted 26 February 2013

Academic Editor: Daoyi Dong

Copyright © 2013 Osman Rasit Isik and Mehmet Sezer. 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

The purpose of this study is to present an approximate solution that depends on collocation points and Bernstein polynomials for a class of Lane-Emden type equations with mixed conditions. The method is given with some priori error estimate. Even the exact solution is unknown, an upper bound based on the regularity of the exact solution will be obtained. By using the residual correction procedure, the absolute error can be estimated. Also, one can specify the optimal truncation limit which gives a better result in any norm. Finally, the effectiveness of the method is illustrated by some numerical experiments. Numerical results are consistent with the theoretical results.