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ISRN Astronomy and Astrophysics
Volume 2011 (2011), Article ID 351747, 7 pages
Research Article

Solution of the Lane-Emden Equation Using the Bernstein Operational Matrix of Integration

1Department of Mathematics, PDPM Indian Institute of Information Technology, Design and Manufacturing Jabalpur, Airport Road, Madhya Pardish, Jabalpur 482005, India
2Department of Mathematics (DIPMAT), University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

Received 28 November 2011; Accepted 22 December 2011

Academic Editors: M. Ding and J. Robertson

Copyright © 2011 Narayan Kumar 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.


Lane-Emden's equation has fundamental importance in the recent analysis of many problems in relativity and astrophysics including some models of density profiles for dark matter halos. An efficient numerical method is presented for linear and nonlinear Lane-Emden-type equations using the Bernstein polynomial operational matrix of integration. The proposed approach is different from other numerical techniques as it is based on the Bernstein polynomial integration matrix. Some illustrative examples are given to demonstrate the efficiency and validity of the proposed algorithm.