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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 641918, 6 pages
http://dx.doi.org/10.1155/2014/641918
Research Article

Lie Group Method of the Diffusion Equations

1Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou 570228, China
2Department of Physics, East China University of Science and Technology, Shanghai 200237, China

Received 1 January 2014; Accepted 7 April 2014; Published 29 April 2014

Academic Editor: Shi-Hai Dong

Copyright © 2014 Jian-Qiang Sun 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

The diffusion equation is discretized in spacial direction and transformed into the ordinary differential equations. The ordinary differential equations are solved by Lie group method and the explicit Runge-Kutta method. Numerical results showed that Lie group method is more stable than the corresponding explicit Runge-Kutta method.