广东工业大学学报 ›› 2024, Vol. 41 ›› Issue (05): 119-124.doi: 10.12052/gdutxb.230048

• 微分方程及其应用 • 上一篇    下一篇

二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式紧致差分格式

关凯菁, 莫艳, 汪志波   

  1. 广东工业大学 数学与统计学院, 广东 广州 510520
  • 收稿日期:2023-03-13 出版日期:2024-09-25 发布日期:2024-05-25
  • 通信作者: 汪志波(1987-),男,教授,主要研究方向为微分方程数值解,E-mail:wzbmath@gdut.edu.cn
  • 作者简介:关凯菁(1999-),女,硕士研究生,主要研究方向为微分方程数值解,E-mail:guankj220@163.com
  • 基金资助:
    国家自然科学基金资助项目(11701103)；广东省珠江人才计划项目(2017GC010379)；广东省自然科学基金资助项目(2022A1515012147，2023A1515011504)；广州市科技计划一般项目(202102020704)

A Compact ADI Scheme for Two-dimensional Caputo-Hadamard Fractional Sub-diffusion Equations

Guan Kai-jing, Mo Yan, Wang Zhi-bo   

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2023-03-13 Online:2024-09-25 Published:2024-05-25

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摘要： 本文讨论了二维时间分数阶Caputo-Hadamard慢扩散方程的交替方向隐式(Alternating Direction Implicit,ADI) 紧致差分格式。首先，在指数型网格上对Caputo-Hadamard型分数阶导数进行离散；其次，利用紧致ADI方法将高维问题转化为2个一维问题；根据离散系数的性质，利用数学归纳法证明了差分格式的稳定性和收敛性；最后，对具体模型进行数值求解。算例验证了上述理论分析的有效性。

关键词: Caputo-Hadamard慢扩散方程, 指数型网格, 紧致交替隐式方法, 稳定性和收敛性

Abstract: The compact alternating direction implicit (ADI) scheme for two-dimensional Caputo-Hadamard fractional sub-differential equations is studied. Firstly, the Caputo-Hadamard fractional derivative on exponential type meshes is approximated. Secondly, in order to solve the high-dimensional problems, a compact ADI method is proposed. With the help of mathematical induction and the properties of discrete coefficients, the stability and convergence of the proposed scheme are analyzed. Ultimately, an example is presented to show the effective of our analysis.

Key words: Caputo-Hadamard fractional differential equations, exponential type meshes, compact alternating direction implicit method, stability and convergence

中图分类号: 

  • O241.8
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