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

页码：578 / 595

页数：18

共 50 条

[1] Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations
Huang, Yun-Chi
Lei, Siu-Long
[J]. NUMERICAL ALGORITHMS, 2020, 84 (01) : 37 - 62
[2] Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equations
Yun-Chi Huang
Siu-Long Lei
[J]. Numerical Algorithms, 2020, 84 : 37 - 62
[3] Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One- and Two-Dimensions
Yu Wang
Min Cai
[J]. Communications on Applied Mathematics and Computation, 2023, 5 : 1674 - 1696
[4] Finite Difference Schemes for Time-Space Fractional Diffusion Equations in One- and Two-Dimensions
Wang, Yu
Cai, Min
[J]. COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2023, 5 (04) : 1674 - 1696
[5] Fourth order finite difference schemes for time-space fractional sub-diffusion equations
Pang, Hong-Kui
Sun, Hai-Wei
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 71 (06) : 1287 - 1302
[6] Finite difference scheme for the time-space fractional diffusion equations
Cao, Jianxiong
Li, Changpin
[J]. CENTRAL EUROPEAN JOURNAL OF PHYSICS, 2013, 11 (10): : 1440 - 1456
[7] Finite difference/finite element method for two-dimensional time-space fractional Bloch-Torrey equations with variable coefficients on irregular convex domains
Xu, Tao
Liu, Fawang
Lu, Shujuan
Anh, Vo V.
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 80 (12) : 3173 - 3192
[8] An implicit difference scheme with the KPS preconditioner for two-dimensional time-space fractional convection-diffusion equations
Zhou, Yongtao
Zhang, Chengjian
Brugnano, Luigi
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 80 (01) : 31 - 42
[9] A preconditioned implicit difference scheme for semilinear two-dimensional time-space fractional Fokker-Planck equations
Zhang, Chengjian
Zhou, Yongtao
[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2021, 28 (04)
[10] Finite difference/finite element method for two-dimensional space and time fractional Bloch-Torrey equations
Bu, Weiping
Tang, Yifa
Wu, Yingchuan
Yang, Jiye
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 264 - 279

← 1 2 3 4 5 →