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All-at-once method for variable-order time fractional diffusion equations
Pang, Hong Kui1; Qin, Hai Hua2; Sun, Hai Wei3
2022-05
Source PublicationNumerical Algorithms
ISSN1017-1398
Volume90Issue:1Pages:31-57
Abstract

We propose a fast solver for the variable-order (VO) time-fractional diffusion equation. Due to the impact of the time-dependent VO function, the resulting coefficient matrix of the large linear system assembling discrete equations of all time levels is a block lower triangular matrix without the block Toeplitz structure. Here, we approximate the off-diagonal blocks by low-rank matrices based on the polynomial interpolation, which can be constructed in O(MlogM) operations with the same number storage requirement, where M is the number of time steps. Furthermore, a divide-and-conquer method is developed to fast solve the approximated linear system. The proposed solver can be implemented in O(NMlogM) complexity with N being the degree of freedom in space. The accuracy of approximation is theoretically studied, and the stability and convergence of the proposed fast method are also investigated. Numerical experiments are carried out to exemplify the accuracy and efficiency of the proposed method.

KeywordAll-at-once Divide-and-conquer Finite Difference Method Low-rank Polynomial Interpolation Vo Time Fractional Derivative
DOI10.1007/s11075-021-01178-7
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000684754100001
Scopus ID2-s2.0-85112414256
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Citation statistics
Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorPang, Hong Kui; Qin, Hai Hua; Sun, Hai Wei
Affiliation1.School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, 221116, China
2.School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China
3.Department of Mathematics, University of Macau, Macao
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Pang, Hong Kui,Qin, Hai Hua,Sun, Hai Wei. All-at-once method for variable-order time fractional diffusion equations[J]. Numerical Algorithms,2022,90(1):31-57.
APA Pang, Hong Kui,Qin, Hai Hua,&Sun, Hai Wei.(2022).All-at-once method for variable-order time fractional diffusion equations.Numerical Algorithms,90(1),31-57.
MLA Pang, Hong Kui,et al."All-at-once method for variable-order time fractional diffusion equations".Numerical Algorithms 90.1(2022):31-57.
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