Numerical Algorithm for the Time-Caputo and Space-Riesz Fractional Difusion Equation

doi:10.1007/s42967-019-00032-x

Communications on Applied Mathematics and Computation ›› 2020, Vol. 2 ›› Issue (1): 57-72.doi: 10.1007/s42967-019-00032-x

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Numerical Algorithm for the Time-Caputo and Space-Riesz Fractional Difusion Equation

Yuxin Zhang, Hengfei Ding

School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China

收稿日期:2019-01-30 修回日期:2019-04-21 出版日期:2020-03-20 发布日期:2020-02-19
通讯作者: Hengfei Ding E-mail:dinghf05@163.com
基金资助:
The work was partially supported by the National Natural Science Foundation of China (no. 11561060).

Numerical Algorithm for the Time-Caputo and Space-Riesz Fractional Difusion Equation

Yuxin Zhang, Hengfei Ding

School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China

Received:2019-01-30 Revised:2019-04-21 Online:2020-03-20 Published:2020-02-19
Contact: Hengfei Ding E-mail:dinghf05@163.com
Supported by:
The work was partially supported by the National Natural Science Foundation of China (no. 11561060).

摘要/Abstract

摘要： In this paper, we develop a novel fnite-diference scheme for the time-Caputo and spaceRiesz fractional difusion equation with convergence order O(τ_2-α + h²). The stability and convergence of the scheme are analyzed by mathematical induction. Moreover, some numerical results are provided to verify the efectiveness of the developed diference scheme.

关键词: Caputo derivative, Riesz derivative, Fractional difusion equation

Abstract: In this paper, we develop a novel fnite-diference scheme for the time-Caputo and spaceRiesz fractional difusion equation with convergence order O(τ_2-α + h²). The stability and convergence of the scheme are analyzed by mathematical induction. Moreover, some numerical results are provided to verify the efectiveness of the developed diference scheme.

Key words: Caputo derivative, Riesz derivative, Fractional difusion equation

中图分类号:

65M06
65M12

Yuxin Zhang, Hengfei Ding. Numerical Algorithm for the Time-Caputo and Space-Riesz Fractional Difusion Equation[J]. Communications on Applied Mathematics and Computation, 2020, 2(1): 57-72.

参考文献

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Numerical Algorithm for the Time-Caputo and Space-Riesz Fractional Difusion Equation

Numerical Algorithm for the Time-Caputo and Space-Riesz Fractional Difusion Equation

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