Journal of Applied Mathematics
Volume 2013 (2013), Article ID 586870, 7 pages
http://dx.doi.org/10.1155/2013/586870
Research Article

Numerical Simulations for the Space-Time Variable Order Nonlinear Fractional Wave Equation

Nasser Hassan Sweilam1 and Taghreed Abdul Rahman Assiri2

1Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
2Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia

Received 3 March 2013; Revised 29 April 2013; Accepted 3 May 2013

Academic Editor: Chein-Shan Liu

Copyright © 2013 Nasser Hassan Sweilam and Taghreed Abdul Rahman Assiri. 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 explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered. The concept of variable order fractional derivative is considered in the sense of Caputo. The stability analysis and the truncation error of the method are discussed. To demonstrate the effectiveness of the method, some numerical test examples are presented.