Weighted finite difference methods for a class of space fractional partial differential equations with variable coefficients

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article

Ding, Zhiqing¹  Xiao, Aiguo¹  Li, Min² 

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[2] Acad Sinica, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100080, Peoples R China

关键词: Left-handed fractional derivative;    Right-handed fractional derivative;    Shifted Grunwald formula;    Weighted finite difference methods;    Stability;    Convergence;   

DOI  :  10.1016/j.cam.2009.09.027

来源: Elsevier

【 摘 要 】

A class of weighted finite difference methods (WFDMs) for solving a class of initial-boundary value problems of space fractional partial differential equations with variable coefficients is presented. Their stability and convergence properties are considered. It is proven that the WFDMs are unconditionally-stable for 0 <= r <= 1/2, and conditionally-stable for 1/2 < r <= 1, here r is the weighting parameter subjected to 0 <= r <= 1. Some convergence results are given. These methods, problems and results generalize the corresponding methods, problems and results given in [7,13,10]. Some numerical examples are provided to show the effectiveness of the methods with different weighting parameters. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free