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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 548292, 11 pages
http://dx.doi.org/10.1155/2012/548292
Research Article

A Characteristic Difference Scheme for Time-Fractional Heat Equations Based on the Crank-Nicholson Difference Schemes

Department of Mathematics, Fatih University, Buyukcekmece, 34500 Istanbul, Turkey

Received 25 April 2012; Revised 27 August 2012; Accepted 27 August 2012

Academic Editor: Dumitru Bǎleanu

Copyright © 2012 Ibrahim Karatay and Serife R. Bayramoglu. 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

We consider the numerical solution of a time-fractional heat equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with Riemann-Liouville fractional derivative of order α, where . The main purpose of this work is to extend the idea on Crank-Nicholson method to the time-fractional heat equations. We prove that the proposed method is unconditionally stable, and the numerical solution converges to the exact one with the order . Numerical experiments are carried out to support the theoretical claims.