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A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations

Author

Listed:
  • Sun, Lu-Yao
  • Fang, Zhi-Wei
  • Lei, Siu-Long
  • Sun, Hai-Wei
  • Zhang, Jia-Li

Abstract

In this paper, a fast algorithm is proposed for solving distributed-order time-space fractional diffusion equations. Integral terms in time and space directions are discretized by the Gauss-Legendre quadrature formula. The Caputo fractional derivatives are approximated by the exponential-sum-approximation method, and the finite difference method is applied for spatial approximation. The coefficient matrix of the discretized linear system is symmetric positive definite and possesses block-Toeplitz-Toeplitz-block structure. The preconditioned conjugate gradient method with a block-circulant-circulant-block preconditioner is employed to solve the linear system. Theoretically, the stability and convergence of the proposed scheme are discussed. Numerical experiments are carried out to demonstrate the effectiveness of the scheme.

Suggested Citation

  • Sun, Lu-Yao & Fang, Zhi-Wei & Lei, Siu-Long & Sun, Hai-Wei & Zhang, Jia-Li, 2022. "A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001795
    DOI: 10.1016/j.amc.2022.127095
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    References listed on IDEAS

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    1. Wang, Xiuping & Gao, Fuzheng & Liu, Yang & Sun, Zhengjia, 2020. "A Weak Galerkin Finite Element Method for High Dimensional Time-fractional Diffusion Equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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    Cited by:

    1. Sun, Lu-Yao & Lei, Siu-Long & Sun, Hai-Wei & Zhang, Jia-Li, 2023. "An α-robust fast algorithm for distributed-order time–space fractional diffusion equation with weakly singular solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 437-452.
    2. Zhang, Meihui & Jia, Jinhong & Zheng, Xiangcheng, 2023. "Numerical approximation and fast implementation to a generalized distributed-order time-fractional option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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