Spectral direction splitting methods for two-dimensional space fractional diffusion equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:299

Article

Xu, Chuanju¹ 

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

关键词: Fractional diffusion equation;    Spectral method;    Direction splitting method;   

DOI  :  10.1016/j.jcp.2015.07.011

来源: Elsevier

【 摘 要 】

A numerical method for a kind of time-dependent two-dimensional two-sided space fractional diffusion equations is developed in this paper. The proposed method combines a time scheme based on direction splitting approaches and a spectral method for the spatial discretization. The direction splitting approach renders the underlying two-dimensional equation into a set of one-dimensional space fractional diffusion equations at each time step. Then these one-dimensional equations are solved by using the spectral method based on weak formulations. A time error estimate is derived for the semi-discrete solution, and the unconditional stability of the fully discretized scheme is proved. Some numerical examples are presented to validate the proposed method. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free