A fast method for variable-order space-fractional diffusion equations

被引：22

作者：

Jia, Jinhong ^{[1
]}

Zheng, Xiangcheng ^{[2
]}

Fu, Hongfei ^{[3
]}

Dai, Pingfei ^{[4
]}

Wang, Hong ^{[2
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250358, Shandong, Peoples R China

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

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

[4] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2020年 / 85卷 / 04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：

Variable-order space-fractional diffusion equation; Collocation method; Divide-and-conquer algorithm; Toeplitz matrix; PRECONDITIONED ITERATIVE METHODS; NUMERICAL APPROXIMATION; VARIATIONAL FORMULATION; DIFFERENTIAL-EQUATIONS; LINEAR-SYSTEMS; TOEPLITZ-LIKE; DISPERSION; REGULARITY; WELLPOSEDNESS;

D O I：

10.1007/s11075-020-00875-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a fast divide-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due to the impact of the space-dependent variable order, the resulting stiffness matrix of the numerical scheme does not have a Toeplitz structure. In this paper, we derive a fast approximation of the coefficient matrix by the means of a finite sum of Toeplitz matrices multiplied by diagonal matrices. We show that the approximation is asymptotically consistent with the original problem, which requires O(Nlog2N)\ memory and O(Nlog3N) computational complexity with N being the numbers of unknowns. Numerical experiments are presented to demonstrate the effectiveness and the efficiency of the proposed method.

引用

页码：1519 / 1540

页数：22

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