Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 730465, 11 pages
doi:10.1155/2009/730465
Research Article

On the Numerical Solution of Fractional Hyperbolic Partial Differential Equations

Allaberen Ashyralyev,1,2 Fadime Dal,3 and Zehra Pinar3

1Department of Mathematics, Fatih University, Buyukcekmece, 34500 Istanbul, Turkey
2Department of Mathematics, ITTU, 744012 Ashgabat, Turkmenistan
3Department of Mathematics, Ege University, 35100 Izmir, Turkey

Received 26 February 2009; Accepted 17 July 2009

Academic Editor: Paulo Batista Gonçalves

Copyright © 2009 Allaberen Ashyralyev 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 stable difference scheme for the numerical solution of the mixed problem for the multidimensional fractional hyperbolic equation is presented. Stability estimates for the solution of this difference scheme and for the first and second orders difference derivatives are obtained. A procedure of modified Gauss elimination method is used for solving this difference scheme in the case of one-dimensional fractional hyperbolic partial differential equations.