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Exponential-sum-approximation technique for variable-order time-fractional diffusion equations
Zhang, Jia Li; Fang, Zhi Wei; Sun, Hai Wei
2022-02-01
Source PublicationJournal of Applied Mathematics and Computing
ISSN1598-5865
Volume68Issue:1Pages:323-347
Abstract

In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function α(t) ∈ (0 , 1) , we develop an exponential-sum-approximation (ESA) technique to approach the VO Caputo fractional derivative. The ESA technique keeps both the quadrature exponents and the number of exponentials in the summation unchanged at different time level. Approximating parameters are properly selected to achieve the efficient accuracy. Compared with the general direct method, the proposed method reduces the storage requirement from O(n) to O(log n) and the computational cost from O(n) to O(nlog n) , respectively, with n being the number of the time levels. When this fast algorithm is exploited to construct a fast ESA scheme for the VO time-fractional diffusion equations, the computational complexity of the proposed scheme is only of O(mnlog n) with O(mlog n) storage requirement, where m denotes the number of spatial grid points. Theoretically, the unconditional stability and error analysis of the fast ESA scheme are given. The effectiveness of the proposed algorithm is verified by numerical examples.

KeywordExponential-sum-approximation Method Fast Algorithm Stability And Convergence Time-fractional Diffusion Equation Variable-order Caputo Fractional Derivative
DOI10.1007/s12190-021-01528-7
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000632851600001
Scopus ID2-s2.0-85103191249
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Cited Times [WOS]:12   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorSun, Hai Wei
AffiliationDepartment of Mathematics, University of Macau, Macao
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Zhang, Jia Li,Fang, Zhi Wei,Sun, Hai Wei. Exponential-sum-approximation technique for variable-order time-fractional diffusion equations[J]. Journal of Applied Mathematics and Computing,2022,68(1):323-347.
APA Zhang, Jia Li,Fang, Zhi Wei,&Sun, Hai Wei.(2022).Exponential-sum-approximation technique for variable-order time-fractional diffusion equations.Journal of Applied Mathematics and Computing,68(1),323-347.
MLA Zhang, Jia Li,et al."Exponential-sum-approximation technique for variable-order time-fractional diffusion equations".Journal of Applied Mathematics and Computing 68.1(2022):323-347.
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