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A transformed L1 method for solving the multi-term time-fractional diffusion problem
She, Mianfu1; Li, Dongfang1,2; Sun, Hai wei3
2022-03-01
Source PublicationMathematics and Computers in Simulation
ISSN0378-4754
Volume193Pages:584-606
Abstract

In this paper, we present a novel scheme for solving a time-fractional initial–boundary value problem, where the equation contains a sum of Caputo derivatives with orders between 0 and 1. In order to overcome the difficulty of initial layer, we introduce a change of variable in the temporal direction and investigate the regularity of the solutions of the resulting system. A modified L1 approximation is used to approximate the Caputo derivatives and a standard Galerkin-Spectral method is applied to approximate the spatial derivatives. Unconditional stability and convergence of the fully-discrete scheme are proved by applying a novel discrete fractional Grönwall inequality. Finally, numerical examples are given to confirm our theoretical results.

KeywordChebyshev–galerkin Spectral Method Error Estimates Modified L1 Scheme Multi-term Time-fractional Equation
DOI10.1016/j.matcom.2021.11.005
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Interdisciplinary Applications ; Computer Science, Software Engineering ; Mathematics, Applied
WOS IDWOS:000789223300010
Scopus ID2-s2.0-85119523030
Fulltext Access
FWCI6.332875
Citation statistics
Cited Times [WOS]:6   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorLi, Dongfang
Affiliation1.School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China
2.Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China
3.Department of Mathematics, University of Macau, Macao, Macao
Recommended Citation
GB/T 7714
She, Mianfu,Li, Dongfang,Sun, Hai wei. A transformed L1 method for solving the multi-term time-fractional diffusion problem[J]. Mathematics and Computers in Simulation,2022,193:584-606.
APA She, Mianfu,Li, Dongfang,&Sun, Hai wei.(2022).A transformed L1 method for solving the multi-term time-fractional diffusion problem.Mathematics and Computers in Simulation,193,584-606.
MLA She, Mianfu,et al."A transformed L1 method for solving the multi-term time-fractional diffusion problem".Mathematics and Computers in Simulation 193(2022):584-606.
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