Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 696179, 15 pages
http://dx.doi.org/10.1155/2012/696179
Research Article

On the Numerical Solution of Fractional Parabolic Partial Differential Equations with the Dirichlet Condition

Allaberen Ashyralyev1,2 and Zafer Cakir3

1Department of Mathematics, Fatih University, Buyukcekmece, 34500 Istanbul, Turkey
2Department of Mathematics, ITTU, Ashgabat, Turkmenistan, Turkey
3Department of Mathematical Engineering, Gumushane University, 29100 Gumushane, Turkey

Received 13 April 2012; Revised 14 June 2012; Accepted 12 July 2012

Academic Editor: Seenith Sivasundaram

Copyright © 2012 Allaberen Ashyralyev and Zafer Cakir. 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 first and second order of accuracy stable difference schemes for the numerical solution of the mixed problem for the fractional parabolic equation are presented. Stability and almost coercive stability estimates for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of one-dimensional fractional parabolic partial differential equations.