An unconditionally convergent RSCSCS iteration method for Riesz space fractional diffusion equations with variable coefficients

Zi-Hang She, Li-Min Qiu and Wei Qu

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 203, issue C, 633-646

Abstract: In this paper, a respectively scaled circulant and skew-circulant splitting (RSCSCS) iteration method is employed to solve the Toeplitz-like linear systems arising from time-dependent Riesz space fractional diffusion equations with variable coefficients. The RSCSCS iteration method is shown to be convergent unconditionally by a novel technique, and only requires computational costs of O(NlogN) with N denoting the number of interior mesh points in space. In theory, we obtain an upper bound for the convergence factor of the RSCSCS iteration method and discuss the optimal value of its iteration parameter that minimizes the corresponding upper bound. Meanwhile, we also design a fast induced RSCSCS preconditioner to accelerate the convergence rate of the Krylov subspace iteration method likes generalized minimal residual (GMRES) method. Numerical results are presented to show that the efficiencies of our proposed RSCSCS iteration method and the preconditioned GMRES method with the RSCSCS preconditioner.

Keywords: Riesz space fractional diffusion equations; Circulant and skew-circulant splitting; Unconditional convergence; Preconditioning (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:203:y:2023:i:c:p:633-646

DOI: 10.1016/j.matcom.2022.07.003

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