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Fast algorithms for high-order numerical methods for space-fractional diffusion equations
Lei, Siu-Long; Huang, Yun-Chi
2017
Source PublicationINTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
ISSN0020-7160
Volume94Issue:5Pages:1062-1078
Abstract

In this paper, fast numerical methods for solving space-fractional diffusion equations are studied in two stages. Firstly, a fast direct solver for an implicit finite difference scheme proposed by Hao et al. [A fourth-order approximation of fractional derivatives with its applications, J. Comput. Phys. 281 (2015), pp. 787-805], which is fourth-order accurate in space and second-order accurate in time, is developed based on a circulant-and-skew-circulant (CS) representation of Toeplitz matrix inversion. Secondly, boundary value method with spatial discretization of Hao et al. [A fourth-order approximation of fractional derivatives with its applications, J. Comput. Phys. 281 (2015), pp. 787-805] is adopted to produce a numerical solution with higher order accuracy in time. Particularly, a method with fourth-order accuracy in both space and time can be achieved. GMRES method is employed for solving the discretized linear system with two preconditioners. Based on the CS representation of Toeplitz matrix inversion, the two preconditioners can be applied efficiently, and the convergence rate of the preconditioned GMRES method is proven to be fast. Numerical examples are given to support the theoretical analysis.

KeywordFractional Diffusion Equation Fourth-order Discretization Boundary Value Method Crank-nicolson Preconditioner Block-circulant Preconditioner Gmres Method Circulant- And Skew-circulant Representation Of Toeplitz Matrix Inversion
DOI10.1080/00207160.2016.1149579
URLView the original
Indexed BySCIE
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000396794000014
PublisherTAYLOR & FRANCIS LTD
The Source to ArticleWOS
Fulltext Access
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Cited Times [WOS]:21   [WOS Record]     [Related Records in WOS]
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,Huang, Yun-Chi. Fast algorithms for high-order numerical methods for space-fractional diffusion equations[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2017,94(5):1062-1078.
APA Lei, Siu-Long,&Huang, Yun-Chi.(2017).Fast algorithms for high-order numerical methods for space-fractional diffusion equations.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,94(5),1062-1078.
MLA Lei, Siu-Long,et al."Fast algorithms for high-order numerical methods for space-fractional diffusion equations".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 94.5(2017):1062-1078.
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