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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 129404, 5 pages
http://dx.doi.org/10.1155/2013/129404
Research Article

A Weighted Average Finite Difference Method for the Fractional Convection-Diffusion Equation

School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China

Received 18 January 2013; Revised 8 April 2013; Accepted 3 June 2013

Academic Editor: R. de la Llave

Copyright © 2013 Lijuan Su and Pei Cheng. 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

A weighted average finite difference method for solving the two-sided space-fractional convection-diffusion equation is given, which is an extension of the weighted average method for ordinary convection-diffusion equations. Stability, consistency, and convergence of the new method are analyzed. A simple and accurate stability criterion valid for this method, arbitrary weighted factor, and arbitrary fractional derivative is given. Some numerical examples with known exact solutions are provided.