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A novel $L1$ method for solving the multi-term time-fractional diffusion problem
She, M. F.; Li, D. F.; Sun, H. W.
2022-02-12
Source PublicationMathematics and Computers in Simulation
ISSN0378-4754
Pages584-606
AbstractIn 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.
KeywordMulti-term time-fractional equation Modified L1 scheme Chebyshev–Galerkin spectral method Error estimates
Language英語English
The Source to ArticlePB_Publication
PUB ID62192
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorLi, D. F.
Recommended Citation
GB/T 7714
She, M. F.,Li, D. F.,Sun, H. W.. A novel $L1$ method for solving the multi-term time-fractional diffusion problem[J]. Mathematics and Computers in Simulation,2022:584-606.
APA She, M. F.,Li, D. F.,&Sun, H. W..(2022).A novel $L1$ method for solving the multi-term time-fractional diffusion problem.Mathematics and Computers in Simulation,584-606.
MLA She, M. F.,et al."A novel $L1$ method for solving the multi-term time-fractional diffusion problem".Mathematics and Computers in Simulation (2022):584-606.
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