数学季刊 ›› 2024, Vol. 39 ›› Issue (1): 18-30.doi: 10.13371/j.cnki.chin.q.j.m.2024.01.002

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带分数阶Robin边界条件的时间-空间分数阶扩散方程的有限差分方法

唐忠华, 房少梅   

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
  • 收稿日期:2022-09-05 出版日期:2024-03-30 发布日期:2024-03-30
  • 通讯作者: FANG Shao-mei (1964-), female, native of Guangzhou, Guangdong, professor of South China Agricultural University, engages in partial differential equation. E-mail:dz90@scau.edu.cn
  • 作者简介:TANG Zhong-hua (1996-), male, native of Wushan, Chongqing, graduate student of South China Agricultural University, engages in partial differential equation; FANG Shao-mei (1964-), female, native of Guangzhou, Guangdong, professor of South China Agricultural University, engages in partial differential equation.
  • 基金资助:
     Supported by National Natural Science Foundation of China (Grant No. 11271141).

Implicit Finite Difference Method for Time-Space Caputo-Riesz Fractional Diffusion Equation with Fractional Robin Boundary Conditions

TANG Zhong-hua, FANG Shao-mei   

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
  • Received:2022-09-05 Online:2024-03-30 Published:2024-03-30
  • Contact: FANG Shao-mei (1964-), female, native of Guangzhou, Guangdong, professor of South China Agricultural University, engages in partial differential equation. E-mail:dz90@scau.edu.cn
  • About author:TANG Zhong-hua (1996-), male, native of Wushan, Chongqing, graduate student of South China Agricultural University, engages in partial differential equation; FANG Shao-mei (1964-), female, native of Guangzhou, Guangdong, professor of South China Agricultural University, engages in partial differential equation.
  • Supported by:
     Supported by National Natural Science Foundation of China (Grant No. 11271141).

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摘要： In this paper, an efficient numerical method is proposed to solve the Caputo-Riesz fractional diffusion equation with fractional Robin boundary conditions. We approximate the Riesz space fractional derivatives using the fractional central difference scheme with second-order accurate. A priori estimation of the solution of the numerical scheme is given, and the stability and convergence of the numerical scheme are analyzed. Finally, a numerical example is used to verify the accuracy and efficiency of the numerical method.

关键词:  Fractional boundary conditions, Stability and convergence, Caputo-Riesz fractional diffusion equation

Abstract: In this paper, an efficient numerical method is proposed to solve the Caputo-Riesz fractional diffusion equation with fractional Robin boundary conditions. We approximate the Riesz space fractional derivatives using the fractional central difference scheme with second-order accurate. A priori estimation of the solution of the numerical scheme is given, and the stability and convergence of the numerical scheme are analyzed. Finally, a numerical example is used to verify the accuracy and efficiency of the numerical method.

Key words:  Fractional boundary conditions, Stability and convergence, Caputo-Riesz fractional diffusion equation

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