Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 562385, 15 pages
http://dx.doi.org/10.1155/2011/562385
Research Article

Finite Difference Method for Hyperbolic Equations with the Nonlocal Integral Condition

Allaberen Ashyralyev1,2 and Necmettin Aggez1

1Department of Mathematics, Fatih University, Istanbul 34500, Turkey
2Department of Mathematics, ITTU, Ashgabat 74400, Turkmenistan

Received 12 April 2010; Accepted 4 January 2011

Academic Editor: Leonid Shaikhet

Copyright © 2011 Allaberen Ashyralyev and Necmettin Aggez. 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 stable difference schemes for the approximate solution of the nonlocal boundary value problem for multidimensional hyperbolic equations with dependent in space variable coefficients are presented. Stability of these difference schemes and of the first- and second-order difference derivatives is obtained. The theoretical statements for the solution of these difference schemes for one-dimensional hyperbolic equations are supported by numerical examples.