A PRECONDITIONED FAST FINITE DIFFERENCE METHOD FOR SPACE-TIME FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS

被引：39

作者：

Fu, Hongfei ^{[1
]}

Wang, Hong ^{[2
]}

机构：

[1] China Univ Petr, Coll Sci, Qingdao 266580, Shandong, Peoples R China

[2] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2017年 / 20卷 / 01期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

anomalous diffusion; finite difference method; space-time discretization; space-time fractional diffusion equation; Krylov subspace method; ELEMENT-METHOD; NUMERICAL ALGORITHMS; DIFFUSION-EQUATIONS; ADVECTION; APPROXIMATIONS; DISPERSION; CONVERGENCE; STABILITY; CALCULUS;

D O I：

10.1515/fca-2017-0005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a fast space-time finite difference method for space-time fractional diffusion equations by fully utilizing the mathematical structure of the scheme. A circulant block preconditioner is proposed to further reduce the computational costs. The method has optimal-order memory requirement and approximately linear computational complexity. The method is not lossy, as no compression of the underlying numerical scheme has been employed. Consequently, the method retains the stability, accuracy, and, in particular, the conservation property of the underlying numerical scheme. Numerical experiments are presented to show the efficiency and capacity of long time modelling of the new method.

引用

页码：88 / 116

页数：29

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