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Numerical Algorithms
Published in: Numerical Algorithms 4/2020

04-02-2020 | Original Paper

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

Authors: Jinhong Jia, Xiangcheng Zheng, Hongfei Fu, Pingfei Dai, Hong Wang

Published in: Numerical Algorithms | Issue 4/2020

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Abstract

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 \(O(N\log ^{2} N)\) memory and \(O(N\log ^{3} N)\) computational complexity with N being the numbers of unknowns. Numerical experiments are presented to demonstrate the effectiveness and the efficiency of the proposed method.
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Metadata
Title
A fast method for variable-order space-fractional diffusion equations
Authors
Jinhong Jia
Xiangcheng Zheng
Hongfei Fu
Pingfei Dai
Hong Wang
Publication date
04-02-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 4/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00875-z

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