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

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

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.

Suggested Citation

  • She, Zi-Hang & Qiu, Li-Min & Qu, Wei, 2023. "An unconditionally convergent RSCSCS iteration method for Riesz space fractional diffusion equations with variable coefficients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 633-646.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:633-646
    DOI: 10.1016/j.matcom.2022.07.003
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    1. Zhao, Yanmin & Bu, Weiping & Huang, Jianfei & Liu, Da-Yan & Tang, Yifa, 2015. "Finite element method for two-dimensional space-fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 553-565.
    2. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
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    Cited by:

    1. Yang, Hong & Lao, Cheng-Xue & She, Zi-Hang, 2023. "Fast solution methods for Riesz space fractional diffusion equations with non-separable coefficients," Applied Mathematics and Computation, Elsevier, vol. 445(C).

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