Finite difference scheme for the time-space fractional diffusion equations

被引：13
|
作者：
Cao, Jianxiong [1 ]
Li, Changpin [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
CENTRAL EUROPEAN JOURNAL OF PHYSICS | 2013年 / 11卷 / 10期
关键词：
time-space fractional diffusion equation; difference scheme; stability; convergence; RANDOM-WALK; SUB-DIFFUSION; SUBDIFFUSION; APPROXIMATIONS; STABILITY;
D O I：
10.2478/s11534-013-0261-x
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we derive two novel finite difference schemes for two types of time-space fractional diffusion equations by adopting weighted and shifted Grunwald operator, which is used to approximate the Riemann-Liouville fractional derivative to the second order accuracy. The stability and convergence of the schemes are analyzed via mathematical induction. Moreover, the illustrative numerical examples are carried out to verify the accuracy and effectiveness of the schemes.
引用
收藏
页码：1440 / 1456
页数：17
相关论文
共 50 条
  • [31] A preconditioned fast finite difference scheme for space-fractional diffusion equations in convex domains
    Ning Du
    Hai-Wei Sun
    Hong Wang
    [J]. Computational and Applied Mathematics, 2019, 38
  • [32] Difference numerical solutions for time-space fractional advection diffusion equation
    Zhang, Fangfang
    Gao, Xiaoyang
    Xie, Zhaokun
    [J]. BOUNDARY VALUE PROBLEMS, 2019,
  • [33] Difference numerical solutions for time-space fractional advection diffusion equation
    Fangfang Zhang
    Xiaoyang Gao
    Zhaokun Xie
    [J]. Boundary Value Problems, 2019
  • [34] Trapezoidal scheme for time-space fractional diffusion equation with Riesz derivative
    Arshad, Sadia
    Huang, Jianfei
    Khaliq, Abdul Q. M.
    Tang, Yifa
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 350 : 1 - 15
  • [35] A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives
    Sayyar, Golsa
    Hosseini, Seyed Mohammad
    Mostajeran, Farinaz
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 104 : 34 - 43
  • [36] Backward problem for time-space fractional diffusion equations in Hilbert scales
    Dang Duc Trong
    Dinh Nguyen Duy Hai
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 93 : 253 - 264
  • [37] A compact finite difference scheme for the fractional sub-diffusion equations
    Gao, Guang-hua
    Sun, Zhi-zhong
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 230 (03) : 586 - 595
  • [38] Implicit finite difference approximation for time fractional diffusion equations
    Murio, Diego A.
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (04) : 1138 - 1145
  • [39] Blowup and MLUH stability of time-space fractional reaction-diffusion equations
    Gao, Peng
    Chen, Pengyu
    [J]. ELECTRONIC RESEARCH ARCHIVE, 2022, 30 (09): : 3351 - 3361
  • [40] A Separable Preconditioner for Time-Space Fractional Caputo-Riesz Diffusion Equations
    Lin, Xuelei
    Ng, Michael K.
    Sun, Haiwei
    [J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2018, 11 (04) : 827 - 853
12345