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

doi:10.12052/gdutxb.230048

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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

微分方程及其应用 | 更新时间：2026-05-27

- 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
- A Compact ADI Scheme for Two-dimensional Caputo-Hadamard Fractional Sub-diffusion Equations
- 广东工业大学学报 2024年41卷第5期页码：119-124
- 作者机构：
  
  广东工业大学数学与统计学院,广东,广州,510520
- 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
  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
- 基金信息：
  
  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)
- DOI：10.12052/gdutxb.230048
  中图分类号： O241.8
- 网络首发：2024-09-25，
  
  纸质出版：2024
- 稿件说明：
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关凯菁, 莫艳, 汪志波. 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[J]. 广东工业大学学报, 2024, 41(5): 119-124.

Guan Kai-jing, Mo Yan, Wang Zhi-bo. A Compact ADI Scheme for Two-dimensional Caputo-Hadamard Fractional Sub-diffusion Equations[J]. 2024, 41(5): 119-124.
关凯菁, 莫艳, 汪志波. 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[J]. 广东工业大学学报, 2024, 41(5): 119-124. DOI： 10.12052/gdutxb.230048.

Guan Kai-jing, Mo Yan, Wang Zhi-bo. A Compact ADI Scheme for Two-dimensional Caputo-Hadamard Fractional Sub-diffusion Equations[J]. 2024, 41(5): 119-124. DOI： 10.12052/gdutxb.230048.

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。

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.

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Keywords

references

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