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 Fast solution algorithms for exponentially tempered fractional diffusion equations Lei, Siu-Long ; Fan, Daoying; Chen, Xu 2018-07 Source Publication NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS ISSN 0749-159X Volume 34Issue: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. Keyword Circulant And skew-Circulant Representation Of Toeplitz Inversion Circulant Preconditioner Fast Fourier Transform Tempered Fractional Diffusion Equations Toeplitz Matrix DOI 10.1002/num.22259 URL View the original Indexed By SCI Language 英语 WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000430677500009 Publisher WILEY The Source to Article WOS Fulltext Access Citation statistics Document Type Journal article Collection DEPARTMENT OF MATHEMATICS Affiliation Univ Macau, Dept Math, Macau, Peoples R China First Author Affilication University of Macau Recommended CitationGB/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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