A Fast Second-Order Implicit Difference Method for Time-Space Fractional Advection-Diffusion Equation
 作者： Yong-Liang Zhao,  Ting-Zhu Huang,  Xian-Ming Gu,  Wei-Hua Luo 作者单位： 1School of Mathematical Sciences , University of Electronic Science and Technology of China , Chengdu , Sichuan , P.R. China 2;School of Economic Mathematics/Institute of Mathematics , Southwestern University of Finance and Economics , Chengdu , Sichuan , P.R. China 3;School of Mathematics and Computational Science , Hunan University of Arts and Science , Changde , Hunan , P.R. China 刊名： Numerical Functional Analysis and Optimization, 2020, Vol.41 (3), pp.257-293 来源数据库： Taylor & Francis Journal DOI： 10.1080/01630563.2019.1627369 关键词： Circulant preconditioner;  Fast Fourier transform;  Krylov subspace method;  Linear/nonlinear fractional advection-diffusion equation;  Toeplitz matrix;  Weighted and shifted Grünwald scheme;  L2- formula; 原始语种摘要： Abstract(#br)In this paper, we consider a fast second-order implicit difference method to approximate a class of linear time-space fractional variable coefficients advection-diffusion equation. To begin with, an implicit difference scheme is constructed based on L 2- formula [Alikhanov AA. 2015;280:424–38.] for the temporal discretization and weighted and shifted Grünwald method for the spatial discretization. Then, the unconditional stability of the scheme is proved. We theoretically and numerically show that it converges in the L 2-norm with the optimal order with the time step... τ and mesh size h . Moreover, the same technique is utilized to solve the nonlinear case of this problem. For the purpose of effectively solving these discretized systems, which have Toeplitz structure, two fast Krylov subspace solvers with suitable circulant preconditioners are designed. In each iterative step, these methods reduce the storage requirements of these discretized systems from to and the computational complexity from to where N is the number of grid nodes. Numerical experiments are carried out to demonstrate that these methods are more practical than the traditional direct solvers of the implicit difference methods, in aspects of memory requirement and calculation time.

• inline　顺列式布置
• graphic　图示的
• subspace　子空间
• Space　空格
• computational　计算的
• fractional　分级的
• approximate　近似的
• demonstrate　说明
• technique　技术
• implicit　隐含的