Year: 2025
Author: Xingyang Ye, Junying Cao, Chuanju Xu
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 615–640
Abstract
In this paper, we consider numerical solutions of the fractional diffusion equation with the $α$ order time fractional derivative defined in the Caputo-Hadamard sense. A high order time-stepping scheme is constructed, analyzed, and numerically validated. The contribution of the paper is twofold: 1) regularity of the solution to the underlying equation is investigated, 2) a rigorous stability and convergence analysis for the proposed scheme is performed, which shows that the proposed scheme is $3 + α$ order accurate. Several numerical examples are provided to verify the theoretical statement.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2312-m2023-0098
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 3 : pp. 615–640
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Caputo-Hadamard derivative Fractional differential equations High order scheme Stability and convergence analysis.
Author Details
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$ \alpha $-robust error analysis of two nonuniform schemes for Caputo-Hadamard fractional reaction sub-diffusion problems
Ye, Xingyang
Liu, Xiaoyue
Lyu, Tong
Liu, Chunxiu
Electronic Research Archive, Vol. 33 (2025), Iss. 1 P.353
https://doi.org/10.3934/era.2025018 [Citations: 0]