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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 463746, 17 pages
http://dx.doi.org/10.1155/2012/463746
Research Article

Stability of Difference Schemes for Fractional Parabolic PDE with the Dirichlet-Neumann Conditions

Department of Mathematical Engineering, Gumushane University, 29100 Gumushane, Turkey

Received 25 March 2012; Accepted 3 April 2012

Academic Editor: Allaberen Ashyralyev

Copyright © 2012 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 stable difference schemes for the fractional parabolic equation with Dirichlet and Neumann boundary conditions are presented. Stability estimates and almost coercive stability estimates with ln ( 1 / ( 𝜏 + | | ) ) for the solution of these difference schemes are obtained. A procedure of modified Gauss elimination method is used for solving these difference schemes of one-dimensional fractional parabolic partial differential equations.