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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 784387, 22 pages
Research Article

A Dufort-Frankel Difference Scheme for Two-Dimensional Sine-Gordon Equation

1School of Sciences, Jimei University, Xiamen 361021, China
2Department of Mathematics, University of Chester, Chester CHI 4BJ, UK

Received 11 March 2014; Revised 22 July 2014; Accepted 24 July 2014; Published 29 October 2014

Academic Editor: Victor S. Kozyakin

Copyright © 2014 Zongqi Liang 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 standard Crank-Nicolson finite-difference scheme and a Dufort-Frankel finite-difference scheme are introduced to solve two-dimensional damped and undamped sine-Gordon equations. The stability and convergence of the numerical methods are considered. To avoid solving the nonlinear system, the predictor-corrector techniques are applied in the numerical methods. Numerical examples are given to show that the numerical results are consistent with the theoretical results.