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Fast solution algorithms for exponentially tempered fractional diffusion equations
Lei, Siu-Long; Fan, Daoying; Chen, Xu
2018-07
Source PublicationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN0749-159X
Volume34Issue:4Pages:1301-1323
Abstract

In this article, a fast-iterative method and a fast-direct method is proposed for solving one-dimensional and twodimensional tempered fractional diffusion equations with constant coefficients. The proposed iterative method is accelerated by circulant preconditioning which is shown to converge superlinearly while the proposed direct method is based on circulant and skew-circulant representation for Toeplitz matrix inversion. In one-dimensional case, the operation cost of the proposed methods are both shown to be O( N logN) with O( N) memory requirement in each time step, where N is the number of spatial nodes. With the alternating direction implicit method, it is proven that the proposed fast solution algorithms can be extended to handle two-dimensional tempered fractional diffusion equations withO( N2 logN) operation cost andO( N2) memory requirement in each time step, where the number of spatial nodes in x-direction and y-direction both equal toN. Numerical examples are provided to illustrate the effectiveness and efficiency of the proposed methods.

KeywordCirculant And skew-Circulant Representation Of Toeplitz Inversion Circulant Preconditioner Fast Fourier Transform Tempered Fractional Diffusion Equations Toeplitz Matrix
DOI10.1002/num.22259
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000430677500009
PublisherWILEY
The Source to ArticleWOS
Fulltext Access
Citation statistics
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
AffiliationUniv Macau, Dept Math, Macau, Peoples R China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lei, Siu-Long,Fan, Daoying,Chen, Xu. Fast solution algorithms for exponentially tempered fractional diffusion equations[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2018,34(4):1301-1323.
APA Lei, Siu-Long,Fan, Daoying,&Chen, Xu.(2018).Fast solution algorithms for exponentially tempered fractional diffusion equations.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,34(4),1301-1323.
MLA Lei, Siu-Long,et al."Fast solution algorithms for exponentially tempered fractional diffusion equations".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 34.4(2018):1301-1323.
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