HIGH-ORDER NUMERICAL METHOD FOR SOLVING A SPACE DISTRIBUTED-ORDER TIME-FRACTIONAL DIFFUSION EQUATION  

作　　者：Jing LI Yingying YANG Yingjun JIANG Libo FENG Boling GUO 李景;杨莹莹;姜英军;封利波;郭柏灵(School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,China;School of Mathematical Sciences,Queensland University of Technology,Brisbane,QLD 4001,Australia;Institute of Applied Physics and Computational Mathematics,Beijing 100088,China)

机构地区：[1]School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,China [2]School of Mathematical Sciences,Queensland University of Technology,Brisbane,QLD 4001,Australia [3]Institute of Applied Physics and Computational Mathematics,Beijing 100088,China

出　　处：《Acta Mathematica Scientia》2021年第3期801-826,共26页数学物理学报（B辑英文版）

基　　金：supported by the Natural and Science Foundation Council of China(11771059);Hunan Provincial Natural Science Foundation of China(2018JJ3519);Scientific Research Project of Hunan Provincial office of Education(20A022)。

摘　　要：This article proposes a high-order numerical method for a space distributed-order time-fractional diffusion equation.First,we use the mid-point quadrature rule to transform the space distributed-order term into multi-term fractional derivatives.Second,based on the piecewise-quadratic polynomials,we construct the nodal basis functions,and then discretize the multi-term fractional equation by the finite volume method.For the time-fractional derivative,the finite difference method is used.Finally,the iterative scheme is proved to be unconditionally stable and convergent with the accuracy O(σ^(2)+τ^(2-β)+h^(3)),whereτand h are the time step size and the space step size,respectively.A numerical example is presented to verify the effectiveness of the proposed method.

关 键 词：Space distributed-order equation time-fractional diffusion equation piecewise-quadratic polynomials finite volume method stability and convergence 

分 类 号：O241.82[理学—计算数学]