Finite difference schemes for two-dimensional time-space fractional differential equations

被引：19
|
作者：
Wang, Zhibo [1 ,2 ]
Vong, Seakweng [1 ]
Lei, Siu-Long [1 ]
机构：
[1] Univ Macau, Dept Math, Ave Univ, Taipa, Macau, Peoples R China
[2] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2016年 / 93卷 / 03期
关键词：
65M06; 65M15; 35R11; 65M12; discrete energy method; ADI scheme; two-dimensional fractional differential equation; preconditioned GMRES method; weighted and shifted Grunwald difference operator; IMPLICIT NUMERICAL-METHOD; DIFFUSION-WAVE EQUATION; SUB-DIFFUSION; SUBDIFFUSION EQUATION; APPROXIMATIONS; STABILITY; CIRCULANT;
D O I：
10.1080/00207160.2015.1009902
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, finite difference schemes for differential equations with both temporal and spatial fractional derivatives are studied. When the order of the time fractional derivative is in [GRAPHICS] , an alternating direction implicit (ADI) scheme with second-order accuracy in both space and time is constructed. For equations with time fractional derivatives of order lying in [GRAPHICS] , a scheme is derived and solved by the generalized minimal residual method. We also propose a preconditioner to improve the efficiency for the implementation of the scheme in this situation.
引用
收藏
页码：578 / 595
页数：18
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