A HIGH-ORDER ACCURACY METHOD FOR SOLVING THE FRACTIONAL DIFFUSION EQUATIONS  

作　　者：Maohua Ran Chengjian Zhang 

机构地区：[1]School of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,China [2]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China

出　　处：《Journal of Computational Mathematics》2020年第2期239-253,共15页计算数学（英文）

基　　金：National Natural Science Foundation of China under grants 11801389 and 11571128.

摘　　要：In this paper,an efficient numerical method for solving the general fractional diffusion equations with Riesz fractional derivative is proposed by combining the fractional compact difference operator and the boundary value methods.In order to efficiently solve the generated linear large-scale system,the generalized minimal residual(GMRES)algorithm is applied.For accelerating the convergence rate of the it erative,the St rang-type,Chantype and P-type preconditioners are introduced.The suggested met hod can reach higher order accuracy both in space and in time than the existing met hods.When the used boundary value method is Ak1,K2-stable,it is proven that Strang-type preconditioner is invertible and the spectra of preconditioned matrix is clustered around 1.It implies that the iterative solution is convergent rapidly.Numerical experiments with the absorbing boundary condition and the generalized Dirichlet type further verify the efficiency.

关 键 词：Boundary value method Circulant preconditioner High accuracy Generalized Dirichlet type boundary condition 

分 类 号：O24[理学—计算数学]