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Second-Order and Nonuniform Time-Stepping Schemes for Time Fractional Evolution Equations with Time–Space Dependent Coefficients
Lyu, Pin1; Vong, Seakweng2
2021-11-01
Source PublicationJournal of Scientific Computing
ISSN0885-7474
Volume89Issue:2
Abstract

The numerical analysis of time fractional evolution equations with the second-order elliptic operator including general time–space dependent variable coefficients is challenging, especially when the classical weak initial singularities are taken into account. In this paper, we introduce a concise technique to construct efficient time-stepping schemes with variable time step sizes for two-dimensional time fractional sub-diffusion and diffusion-wave equations with general time–space dependent variable coefficients. By means of the novel technique, the nonuniform Alikhanov type schemes are constructed and analyzed for the sub-diffusion and diffusion-wave problems. For the diffusion-wave problem, our scheme is constructed by employing the recently established symmetric fractional-order reduction method. The unconditional stability of proposed schemes is rigorously discussed under mild assumptions on variable coefficients and, based on reasonable regularity assumptions and weak time mesh restrictions, the second-order convergence is obtained with respect to discrete H-norm. Numerical experiments are given to demonstrate the theoretical statements.

KeywordNonuniform Mesh Time Fractional Evolution Equations Variable Coefficients Weak Singularity
DOI10.1007/s10915-021-01661-2
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000707348900001
Scopus ID2-s2.0-85117332893
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Cited Times [WOS]:3   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorVong, Seakweng
Affiliation1.School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, China
2.Department of Mathematics, University of Macau, Macao
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lyu, Pin,Vong, Seakweng. Second-Order and Nonuniform Time-Stepping Schemes for Time Fractional Evolution Equations with Time–Space Dependent Coefficients[J]. Journal of Scientific Computing,2021,89(2).
APA Lyu, Pin,&Vong, Seakweng.(2021).Second-Order and Nonuniform Time-Stepping Schemes for Time Fractional Evolution Equations with Time–Space Dependent Coefficients.Journal of Scientific Computing,89(2).
MLA Lyu, Pin,et al."Second-Order and Nonuniform Time-Stepping Schemes for Time Fractional Evolution Equations with Time–Space Dependent Coefficients".Journal of Scientific Computing 89.2(2021).
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