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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 293706, 10 pages
http://dx.doi.org/10.1155/2013/293706
Research Article

Maximum Norm Error Estimates of ADI Methods for a Two-Dimensional Fractional Subdiffusion Equation

1Department of Mathematics, East China Normal University, Shanghai 200241, China
2Scientific Computing Key Laboratory of Shanghai Universities, Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai 200234, China

Received 25 June 2013; Accepted 8 July 2013

Academic Editor: Ming Li

Copyright © 2013 Yuan-Ming Wang. 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

This paper is concerned with two alternating direction implicit (ADI) finite difference methods for solving a two-dimensional fractional subdiffusion equation. An explicit error estimate for each of the two methods is provided in the discrete maximum norm. It is shown that the methods have the same order as their truncation errors with respect to the discrete maximum norm. Numerical results are given to confirm the theoretical analysis results.