数学季刊 ›› 2024, Vol. 39 ›› Issue (1): 18-30.doi: 10.13371/j.cnki.chin.q.j.m.2024.01.002
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:
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:摘要： In this paper, an efficient numerical method is proposed to solve the CaputoRiesz 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.
中图分类号:
唐忠华, 房少梅. 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[J]. 数学季刊, 2024, 39(1): 18-30.
TANG Zhong-hua, FANG Shao-mei. Implicit Finite Difference Method for Time-Space Caputo-Riesz Fractional Diffusion Equation with Fractional Robin Boundary Conditions[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 18-30.
| [1] | 邹绵璐, 李强. 贝索夫空间中三维布辛涅斯克方程的一些新的正则性准则[J]. 数学季刊, 2024, 39(1): 73-81. |
| [2] | 郭晋东. 关于两个两点Witten-Kontsevich关联子公式等价的一个注记[J]. 数学季刊, 2024, 39(1): 82-85. |
| [3] | 刘功伟, 杨坤. 一类退化抛物方程高初始能量下解的有限时刻爆破及整体存在性[J]. 数学季刊, 2024, 39(1): 97-110. |
| [4] | 李鸿军. 凸复Finsler流形上的Hopf-Rinow定理[J]. 数学季刊, 2024, 39(1): 31-45. |
| [5] | 洪勇, 赵茜. 两类加权空间间的积分算子与离散算子的有界性及算子范数估计[J]. 数学季刊, 2024, 39(1): 59-67. |
| [6] | 王川, 乔炎. Korteweg-de Vries方程的Legendre时空谱配置方法[J]. 数学季刊, 2023, 38(4): 392-400. |
| [7] | 许娜. 一类次线性基尔霍夫方程基态解的存在性[J]. 数学季刊, 2023, 38(4): 410-414. |
| [8] | 杨亦松. 曲面上的曲率在理论物理中的一些应用[J]. 数学季刊, 2023, 38(3): 221-253. |
| [9] | 徐晓濛. Stokes 现象与量子群的表示[J]. 数学季刊, 2023, 38(3): 311-330. |
| [10] | 黄述亮. 带有对合的素环的微分恒等式[J]. 数学季刊, 2023, 38(2): 134-144. |
| [11] | 马腾. 变指标中心Morrey空间上带Dini核的多线性C-Z算子[J]. 数学季刊, 2023, 38(2): 184-195. |
| [12] | 梁艳霞. 带位势的基尔霍夫方程规范解的存在性[J]. 数学季刊, 2023, 38(2): 196-209. |
| [13] | 白宏芳. 一类具有时滞的生态流行病模型的稳定性与 Hopf 分支[J]. 数学季刊, 2023, 38(2): 157-183. |
| [14] | 杜玲珑, 韩晓岳, 于佳平, 周昕昀. 具有势场的随机Cucker-Smale系统[J]. 数学季刊, 0, (): 111-122. |
| [15] | 柳亮, 王亚强. 非奇异H-张量的新判定[J]. 数学季刊, 2023, 38(2): 123-133. |
| 阅读次数 | ||||||
|
全文 |
|
|||||
|
摘要 |
|
|||||
