HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION

doi:10.1007/s10473-021-0311-1

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 801-826.doi: 10.1007/s10473-021-0311-1

HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION

李景¹, 杨莹莹¹, 姜英军¹, 封利波², 郭柏灵³

1. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China;
2. School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia;
3. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

收稿日期:2019-11-26 修回日期:2020-09-24 出版日期:2021-06-25 发布日期:2021-06-07
通讯作者: Jing LI E-mail:lijingnew@126.com
作者简介:Yingying YANG,E-mail:1720719892@qq.com;Yingjun JIANG,E-mail:jiangyingjun@csust.edu.cn;Libo FENG,E-mail:fenglibo2012@126.com;Boling GUO,E-mail:gbl@iapcm.ac.cn
基金资助:
The first author is supported by the Natural and Science Foundation Council of China (11771059), Hunan Provincial Natural Science Foundation of China (2018JJ3519) and Scientific Research Project of Hunan Provincial office of Education (20A022).

HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION

Jing LI¹, Yingying YANG¹, Yingjun JIANG¹, Libo FENG², Boling GUO³

1. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China;
2. School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia;
3. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2019-11-26 Revised:2020-09-24 Online:2021-06-25 Published:2021-06-07
Contact: Jing LI E-mail:lijingnew@126.com
About author:Yingying YANG,E-mail:1720719892@qq.com;Yingjun JIANG,E-mail:jiangyingjun@csust.edu.cn;Libo FENG,E-mail:fenglibo2012@126.com;Boling GUO,E-mail:gbl@iapcm.ac.cn
Supported by:
The first author is supported by the Natural and Science Foundation Council of China (11771059), Hunan Provincial Natural Science Foundation of China (2018JJ3519) and Scientific Research Project of Hunan Provincial office of Education (20A022).

摘要/Abstract

摘要： This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation. First, we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives. Second, based on the piecewise-quadratic polynomials, we construct the nodal basis functions, and then discretize the multi-term fractional equation by the finite volume method. For the time-fractional derivative, the finite difference method is used. Finally, the iterative scheme is proved to be unconditionally stable and convergent with the accuracy $O(\sigma^2+\tau^{2-\beta}+h^3)$, where $\tau$ and $h$ are the time step size and the space step size, respectively. A numerical example is presented to verify the effectiveness of the proposed method.

关键词: Space distributed-order equation, time-fractional diffusion equation, piecewise-quadratic polynomials, finite volume method, stability and convergence

Abstract: This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation. First, we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives. Second, based on the piecewise-quadratic polynomials, we construct the nodal basis functions, and then discretize the multi-term fractional equation by the finite volume method. For the time-fractional derivative, the finite difference method is used. Finally, the iterative scheme is proved to be unconditionally stable and convergent with the accuracy $O(\sigma^2+\tau^{2-\beta}+h^3)$, where $\tau$ and $h$ are the time step size and the space step size, respectively. A numerical example is presented to verify the effectiveness of the proposed method.

Key words: Space distributed-order equation, time-fractional diffusion equation, piecewise-quadratic polynomials, finite volume method, stability and convergence

中图分类号:

35R11

李景, 杨莹莹, 姜英军, 封利波, 郭柏灵. HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION[J]. 数学物理学报(英文版), 2021, 41(3): 801-826.

Jing LI, Yingying YANG, Yingjun JIANG, Libo FENG, Boling GUO. HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION[J]. Acta mathematica scientia,Series B, 2021, 41(3): 801-826.

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HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION

HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION

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