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research-article

Some high order difference schemes for the space and time fractional Bloch-Torrey equations

Authors:

Guang-hua GaoAuthors Info & Claims

Applied Mathematics and Computation, Volume 281, Issue C

Pages 356 - 380

https://doi.org/10.1016/j.amc.2016.01.044

Published: 30 April 2016 Publication History

Abstract

In this paper, several difference schemes are proposed for both one-dimensional and two-dimensional space and time fractional Bloch-Torrey equations. The spatial second-order scheme and the spatial fourth-order compact scheme are established, respectively. The obtained schemes can achieve the global second-order numerical accuracy in time. The unique solvability, unconditional stability and convergence of the proposed schemes are proved by the energy method. Two ADI schemes are also discussed for the two dimensional problem. Numerical examples are given to verify the numerical accuracy and efficiency of the difference schemes.

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Cited By

Feng XYuan XZhao MQian Z(2024)Numerical methods for the forward and backward problems of a time-space fractional diffusion equationCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-024-00567-361:1Online publication date: 21-Feb-2024
https://dl.acm.org/doi/10.1007/s10092-024-00567-3
Huang YChou LLei S(2023)Divide-and-Conquer Solver in Tensor-Train Format for d-Dimensional Time-Space Fractional Diffusion EquationsJournal of Scientific Computing10.1007/s10915-023-02259-696:1Online publication date: 5-Jun-2023
https://dl.acm.org/doi/10.1007/s10915-023-02259-6
Hao ZCao WLi S(2021)Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularityNumerical Algorithms10.1007/s11075-020-00923-886:3(1071-1087)Online publication date: 1-Mar-2021
https://dl.acm.org/doi/10.1007/s11075-020-00923-8
Show More Cited By

Some high order difference schemes for the space and time fractional Bloch-Torrey equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
    2. Numerical analysis
2. Theory of computation

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Published In

cover image Applied Mathematics and Computation

Applied Mathematics and Computation Volume 281, Issue C

April 2016

403 pages

ISSN:0096-3003

Issue’s Table of Contents

Copyright © Elsevier Inc.

Publisher

Elsevier Science Inc.

United States

Publication History

Published: 30 April 2016

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Cited By

Feng XYuan XZhao MQian Z(2024)Numerical methods for the forward and backward problems of a time-space fractional diffusion equationCalcolo: a quarterly on numerical analysis and theory of computation10.1007/s10092-024-00567-361:1Online publication date: 21-Feb-2024
https://dl.acm.org/doi/10.1007/s10092-024-00567-3
Huang YChou LLei S(2023)Divide-and-Conquer Solver in Tensor-Train Format for d-Dimensional Time-Space Fractional Diffusion EquationsJournal of Scientific Computing10.1007/s10915-023-02259-696:1Online publication date: 5-Jun-2023
https://dl.acm.org/doi/10.1007/s10915-023-02259-6
Hao ZCao WLi S(2021)Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularityNumerical Algorithms10.1007/s11075-020-00923-886:3(1071-1087)Online publication date: 1-Mar-2021
https://dl.acm.org/doi/10.1007/s11075-020-00923-8
Abbaszadeh MDehghan M(2021)A finite-difference procedure to solve weakly singular integro partial differential equation with space-time fractional derivativesEngineering with Computers10.1007/s00366-020-00936-w37:3(2173-2182)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1007/s00366-020-00936-w
Huang YLei S(2019)Fast solvers for finite difference scheme of two-dimensional time-space fractional differential equationsNumerical Algorithms10.1007/s11075-019-00742-684:1(37-62)Online publication date: 21-Jun-2019
https://dl.acm.org/doi/10.1007/s11075-019-00742-6
Zhao YBu WZhao XTang Y(2017)Galerkin finite element method for two-dimensional space and time fractional BlochTorrey equationJournal of Computational Physics10.1016/j.jcp.2017.08.051350:C(117-135)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1016/j.jcp.2017.08.051
Huang YLei S(2017)A fast numerical method for block lower triangular Toeplitz with dense Toeplitz blocks system with applications to time-space fractional diffusion equationsNumerical Algorithms10.1007/s11075-017-0272-676:3(605-616)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1007/s11075-017-0272-6

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