Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 434976, 15 pages
http://dx.doi.org/10.1155/2012/434976
Research Article

Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition

Allaberen Ashyralyev1,2 and Fadime Dal3

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

Received 19 December 2011; Accepted 18 April 2012

Academic Editor: Chuanxi Qian

Copyright © 2012 Allaberen Ashyralyev and Fadime Dal. 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 numerical and analytic solutions of the mixed problem for multidimensional fractional hyperbolic partial differential equations with the Neumann condition are presented. The stable difference scheme for the numerical solution of the mixed problem for the multidimensional fractional hyperbolic equation with the Neumann condition is presented. Stability estimates for the solution of this difference scheme and for the first- and second-order 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. He's variational iteration method is applied. The comparison of these methods is presented.