A note on efficient preconditioner of implicit Runge–Kutta methods with application to fractional diffusion equations

Hao Chen, Xiaoli Wang and Xiaolin Li

Applied Mathematics and Computation, 2019, vol. 351, issue C, 116-123

Abstract: This paper is concerned with the construction of efficient preconditioning method for systems arising from implicit Runge–Kutta discretizations of time-dependent PDEs. A polynomial preconditioner is proposed based on the Kronecker product splitting iteration method introduced by Chen (BIT 54:607-721, 2014). Some useful properties on the spectrum of the preconditioned matrix are established. Numerical experiments concerning discrete solution of fractional diffusion equations are presented to show the effectiveness of the proposed polynomial preconditioner.

Keywords: Fractional diffusion equations; Implicit Runge–Kutta methods; Iterative methods; Preconditioning; Kronecker product splitting (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:351:y:2019:i:c:p:116-123

DOI: 10.1016/j.amc.2019.01.041

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