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10-07-2019 | Original Paper | Issue 2/2020

Preconditioned quasi-compact boundary value methods for space-fractional diffusion equations

Journal:: Numerical Algorithms > Issue 2/2020

Authors:: Yongtao Zhou, Chengjian Zhang, Luigi Brugnano

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Abstract

This paper focuses on highly efficient numerical methods for solving space-fractional diffusion equations. By combining the fourth-order quasi-compact difference scheme and boundary value methods, a class of quasi-compact boundary value methods are constructed. In order to accelerate the convergence rate of this class of methods, the Kronecker product splitting (KPS) iteration method and the preconditioned method with KPS preconditioner are proposed. A convergence criterion for the KPS iteration method is derived. A numerical experiment further illustrates the computational efficiency and accuracy of the proposed methods. Moreover, a numerical comparison with the preconditioned method with Strang-type preconditioner is given, which shows that the preconditioned method with KPS preconditioner is comparable in computational efficiency.

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Title: Preconditioned quasi-compact boundary value methods for space-fractional diffusion equations
Authors:: Yongtao Zhou
Chengjian Zhang
Luigi Brugnano
Publication date: 10-07-2019
DOI: https://doi.org/10.1007/s11075-019-00773-z
Publisher: Springer US
Journal: Numerical Algorithms
Issue 2/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265

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