A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives

被引：6

作者：

Sayyar, Golsa ^{[1
]}

Hosseini, Seyed Mohammad ^{[1
]}

Mostajeran, Farinaz ^{[1
]}

机构：

[1] Tarbiat Modares Univ, Fac Math Sci, Dept Appl Math, POB 14115-175, Tehran, Iran

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 104卷

关键词：

Caputo derivative; Fractional diffusion equation; Riesz derivative; Fractional kinetic equation; Weighted and shifted Grunwald difference method; BOUNDARY-VALUE-PROBLEMS; FINITE-ELEMENT-METHOD; DIFFERENCE-METHODS; SPECTRAL METHOD;

D O I：

10.1016/j.camwa.2021.11.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a high-order approach for solving one- and two-dimensional time-space fractional diffusion equations (FDEs) with Caputo-Riesz derivatives. To design the scheme, the Caputo temporal derivative is approximated using a high-order method, and the spatial Riesz derivative is discretized by the second-order weighted and shifted Grunwald difference (WSGD) method. It is proved that the scheme is unconditionally stable and convergent with the order of O (tau(alpha)h(2) + tau(4) ), where tau and h are time and space step sizes, respectively. We illustrate the accuracy and effectiveness of the method by providing several numerical examples.

引用

页码：34 / 43

页数：10

共 50 条

[21] High-Order Methods for Systems of Fractional Ordinary Differential Equations and Their Application to Time-Fractional Diffusion Equations [J].

Ferras, Luis L. ;

Ford, Neville ;

Morgado, Maria Luisa ;

Rebelo, Magda .

MATHEMATICS IN COMPUTER SCIENCE, 2021, 15 (04) :535-551

[22] A Note on Numerical Algorithm for the Time-Caputo and Space-Riesz Fractional Diffusion Equation [J].

Tian, Junhong ;

Ding, Hengfei .

COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2021, 3 (04) :571-584

[23] Higher order class of finite difference method for time-fractional Liouville-Caputo and space-Riesz fractional diffusion equation [J].

Irandoust-Pakchin, Safar ;

Abdi-Mazraeh, Somaiyeh ;

Fahimi-Khalilabad, Iraj .

FILOMAT, 2024, 38 (02) :505-521

[24] Numerical algorithm to Caputo type time-space fractional partial differential equations with variable coefficients [J].

Kheybari, Samad .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2021, 182 :66-85

[25] A novel high-order approximate scheme for two-dimensional time-fractional diffusion equations with variable coefficient [J].

Wang, Fenling ;

Zhao, Yanmin ;

Chen, Chen ;

Wei, Yabing ;

Tang, Yifa .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 78 (05) :1288-1301

[26] High-order algorithm for the two-dimension Riesz space-fractional diffusion equation [J].

Zhang, Yuxin ;

Ding, Hengfei .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2017, 94 (10) :2063-2073

[27] Second-order BDF time approximation for Riesz space-fractional diffusion equations [J].

Liao, Hong-Lin ;

Lyu, Pin ;

Vong, Seakweng .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (01) :144-158

[28] A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain [J].

Zhao, Jingjun ;

Xiao, Jingyu ;

Xu, Yang .

ABSTRACT AND APPLIED ANALYSIS, 2013,

[29] A second-order implicit difference scheme for the nonlinear time-space fractional Schrodinger equation [J].

Fei, Mingfa ;

Wang, Nan ;

Huang, Chengming ;

Ma, Xiaohua .

APPLIED NUMERICAL MATHEMATICS, 2020, 153 :399-411

[30] Numerical algorithms for the time-Caputo and space-Riesz fractional Bloch-Torrey equations [J].

Ding, Hengfei ;

Li, Changpin .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2020, 36 (04) :772-799

← 1 2 3 4 5 →