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Lu, Xin; Pang, Hong-Kui; Sun, Hai-Wei; Vong, Seak-Weng

Approximate inversion method for time-fractional subdiffusion equations. (English) Zbl 1499.65108

Numer. Linear Algebra Appl. 25, No. 2, e2132, 12 p. (2018).
Summary: The finite-difference method applied to the time-fractional subdiffusion equation usually leads to a large-scale linear system with a block lower triangular Toeplitz coefficient matrix. The approximate inversion method is employed to solve this system. A sufficient condition is proved to guarantee the high accuracy of the approximate inversion method for solving the block lower triangular Toeplitz systems, which are easy to verify in practice and have a wide range of applications. The applications of this sufficient condition to several existing finite-difference schemes are investigated. Numerical experiments are presented to verify the validity of theoretical results.

Cited in 16 Documents

MSC:

65F08 Preconditioners for iterative methods
65F05 Direct numerical methods for linear systems and matrix inversion
35R11 Fractional partial differential equations

Keywords:

approximate inversion method; block lower triangular Toeplitz matrix; fast Fourier transforms; matrix polynomial; time-fractional subdiffusion equations

Software:

Matlab
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Full Text: DOI

References:

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