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Publishing Language: Chinese | Open Access

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

Kai-jing Guan, Yan Mo, Zhi-bo Wang( )
School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China
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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.

Keywords

Caputo-Hadamard fractional differential equationsexponential type meshescompact alternating direction implicit methodstability and convergence
CLC number: O241.8

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Journal of Guangdong University of Technology
Volume 41 Issue 5,
September 2024
Pages 119-124
DOI: 10.12052/gdutxb.230048

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Cite this article:
Guan K-j, Mo Y, Wang Z-b. A Compact ADI Scheme for Two-dimensional Caputo-Hadamard Fractional Sub-diffusion Equations. Journal of Guangdong University of Technology, 2024, 41(5): 119-124. https://doi.org/10.12052/gdutxb.230048

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Received: 13 March 2023
Published: 01 September 2024
© 2024 Editorial Office of Journal of Guangdong University of Technology

This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/).