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 Fast algorithms for high-order numerical methods for space-fractional diffusion equations Lei, Siu-Long; Huang, Yun-Chi 2017 Source Publication INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS ISSN 0020-7160 Volume 94Issue: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. Keyword Fractional 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 DOI 10.1080/00207160.2016.1149579 URL View the original Indexed By SCI Language 英语 WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000396794000014 Publisher TAYLOR & FRANCIS LTD The Source to Article WOS 全文获取链接 引用统计 被引频次[WOS]：13   [WOS记录]     [WOS相关记录] Document Type Journal article 专题 DEPARTMENT OF MATHEMATICS Affiliation Univ Macau, Dept Math, Macau, Peoples R China First Author Affilication University of Macau 推荐引用方式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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