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A second-order scheme with nonuniform time grids for Caputo–Hadamard fractional sub-diffusion equations
Wang, Zhibo1; Ou, Caixia1; Vong, Seakweng2
2022-11-01
Source PublicationJournal of Computational and Applied Mathematics
ISSN0377-0427
Volume414
Abstract

In this paper, a second-order scheme with nonuniform time meshes for Caputo–Hadamard fractional sub-diffusion equations with initial singularity is investigated. Firstly, a Taylor-like formula with integral remainder is proposed, which is crucial to studying the discrete convolution kernels and error estimate. Secondly, we come up with an error convolution structure (ECS) analysis for L interpolation approximation to the Caputo–Hadamard fractional derivative. The core result in this paper is an ECS bound and a global consistency analysis established at an offset point. By virtue of this result, we obtain a sharp L-norm error estimate of a second-order Crank–Nicolson-like scheme for Caputo–Hadamard fractional differential equations. Ultimately, an example is presented to show the sharpness of our analysis.

KeywordCaputo–hadamard Derivative Error Convolution Structure Global Consistency Analysis Nonuniform Meshes Weak Singularity
DOI10.1016/j.cam.2022.114448
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000811831800012
Scopus ID2-s2.0-85131423725
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Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorVong, Seakweng
Affiliation1.School of Mathematics and Statistics, Guangdong University of Technology, Guangdong, Guangzhou, 510006, China
2.Department of Mathematics, University of Macau, Macao, China
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Wang, Zhibo,Ou, Caixia,Vong, Seakweng. A second-order scheme with nonuniform time grids for Caputo–Hadamard fractional sub-diffusion equations[J]. Journal of Computational and Applied Mathematics,2022,414.
APA Wang, Zhibo,Ou, Caixia,&Vong, Seakweng.(2022).A second-order scheme with nonuniform time grids for Caputo–Hadamard fractional sub-diffusion equations.Journal of Computational and Applied Mathematics,414.
MLA Wang, Zhibo,et al."A second-order scheme with nonuniform time grids for Caputo–Hadamard fractional sub-diffusion equations".Journal of Computational and Applied Mathematics 414(2022).
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