Weighted average finite difference methods for fractional diffusion equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:216

Article

Yuste, S. B.

关键词: fractional diffusion equation;    von Neumann stability analysis;    finite difference methods;    anomalous diffusion;   

DOI  :  10.1016/j.jcp.2005.12.006

来源: Elsevier

【 摘 要 】

A class of finite difference methods for solving fractional diffusion equations is considered. These methods are an extension of the weighted average methods for ordinary (non-fractional) diffusion equations. Their accuracy is of order (Delta x)(2) and At, except for the fractional version of the Crank Nicholson method, where the accuracy with respect to the timestep is of order (Delta t)(2) if a second-order approximation to the fractional time-derivative is used. Their stability is analyzed by means of a recently proposed procedure akin to the standard von Neumann stability analysis. A simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order of the fractional derivative, is found and checked numerically. Some examples are provided in which the new methods' numerical solutions are obtained and compared against exact solutions. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free