Stability and convergence of a Crank-Nicolson finite volume method for space fractional diffusion equations

被引：29
|
作者：
Fu, Hongfei [1 ]
Sun, Yanan [1 ]
Wang, Hong [2 ]
Zheng, Xiangcheng [2 ]
机构：
[1] China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China
[2] Univ South Carolina, Dept Math, Columbia, SC 29208 USA
来源：
APPLIED NUMERICAL MATHEMATICS | 2019年 / 139卷
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
Fractional diffusion equation; Finite volume method; Crank-Nicolson discretization; Stability and convergence; Preconditioned fast BiCGSTAB method; SPECTRAL METHOD; DIFFERENCE APPROXIMATIONS;
D O I：
10.1016/j.apnum.2019.01.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We analyze a Crank-Nicolson finite volume method (CN-FVM) for the time-dependent two-sided conservative space fractional diffusion equation (of order 2 - alpha). We prove that the proposed method is unconditionally stable in a weighted discrete norm and has a convergence rate of order (sic)(tau(2) + h(1+alpha)), where tau and h are the time step size and spatial mesh size, respectively. In addition, we present a matrix-free preconditioned fast BiCGSTAB solver for the discrete linear algebraic system, which has a linear memory requirement and almost linear computational complexity. Numerical experiments show strong potential of the fast CN-FVM. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：38 / 51
页数：14
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