Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations

doi:10.1007/s42967-019-00033-w

Communications on Applied Mathematics and Computation ›› 2019, Vol. 1 ›› Issue (4): 621-637.doi: 10.1007/s42967-019-00033-w

• ORIGINAL PAPER • 上一篇

Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations

Yubo Yang¹, Fanhai Zeng²

1 Nanhu College, Jiaxing University, Jiaxing 314001, Zhejiang, China;
2 Department of Mathematics, National University of Singapore, Singapore 119076, Singapore

收稿日期:2018-09-23 修回日期:2019-01-16 出版日期:2019-12-30 发布日期:2019-10-16
通讯作者: Fanhai Zeng, Yubo Yang E-mail:fanhaiz@foxmail.com;boydman_xm@mail.zjxu.edu.cn
基金资助:
The authors wish to thank the referees for their constructive comments and suggestions, which greatly improved the quality of this paper.

Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations

Yubo Yang¹, Fanhai Zeng²

1 Nanhu College, Jiaxing University, Jiaxing 314001, Zhejiang, China;
2 Department of Mathematics, National University of Singapore, Singapore 119076, Singapore

Received:2018-09-23 Revised:2019-01-16 Online:2019-12-30 Published:2019-10-16
Contact: Fanhai Zeng, Yubo Yang E-mail:fanhaiz@foxmail.com;boydman_xm@mail.zjxu.edu.cn
Supported by:
The authors wish to thank the referees for their constructive comments and suggestions, which greatly improved the quality of this paper.

摘要/Abstract

摘要： In this paper, a new type of the discrete fractional Grönwall inequality is developed, which is applied to analyze the stability and convergence of a Galerkin spectral method for a linear time-fractional subdiffusion equation. Based on the temporal-spatial error splitting argument technique, the discrete fractional Grönwall inequality is also applied to prove the unconditional convergence of a semi-implicit Galerkin spectral method for a nonlinear time-fractional subdiffusion equation.

关键词: Time-fractional subdiffusion equation, Convolution quadrature, Fractional linear multistep methods, Discrete fractional Gr?nwall inequality, Unconditional stability

Abstract: In this paper, a new type of the discrete fractional Grönwall inequality is developed, which is applied to analyze the stability and convergence of a Galerkin spectral method for a linear time-fractional subdiffusion equation. Based on the temporal-spatial error splitting argument technique, the discrete fractional Grönwall inequality is also applied to prove the unconditional convergence of a semi-implicit Galerkin spectral method for a nonlinear time-fractional subdiffusion equation.

Key words: Time-fractional subdiffusion equation, Convolution quadrature, Fractional linear multistep methods, Discrete fractional Gr?nwall inequality, Unconditional stability

中图分类号:

Yubo Yang, Fanhai Zeng. Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations[J]. Communications on Applied Mathematics and Computation, 2019, 1(4): 621-637.

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Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations

Numerical Analysis of Linear and Nonlinear Time-Fractional Subdiffusion Equations

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