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Journal of Applied Mathematics
Volume 2012, Article ID 163821, 16 pages
Research Article

A Coupled Method of Laplace Transform and Legendre Wavelets for Lane-Emden-Type Differential Equations

1College of Computer, National University of Defense Technology, Changsha 410073, China
2China Aerodynamics Research and Development Center, Sichuan, Mianyang 621000, China

Received 4 September 2012; Revised 11 October 2012; Accepted 15 October 2012

Academic Editor: Sazzad H. Chowdhury

Copyright © 2012 Fukang Yin 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 coupled method of Laplace transform and Legendre wavelets is presented to obtain exact solutions of Lane-Emden-type equations. By employing properties of Laplace transform, a new operator is first introduced and then its Legendre wavelets operational matrix is derived to convert the Lane-Emden equations into a system of algebraic equations. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The results show that the proposed method is very effective and easy to implement.