Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 124129, 13 pages
doi:10.1155/2010/124129
Research Article

The Numerical Convergence of the Landau-Lifshitz Equations and Its Simulation

Penghong Zhong,1 Shu Wang,1 Ke Wang,1 and Yiping Bai2

1Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, China
2South China Sea Marine Prediction Center (SCSMPC), State Oceanic Administration, China

Received 19 December 2009; Accepted 5 March 2010

Academic Editor: Manuel De la Sen

Copyright © 2010 Penghong Zhong 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

A difference scheme of Landau-Lifshitz (LL for short) equations is studied. Their convergence and stability are proved. Furthermore, a new solution of LL equation is given for testing our scheme. At the end, three subcases of this LL equation are concerned about, and some properties about these equations are shown by a numeric simulation way.