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An ADI difference scheme based on fractional trapezoidal rule for fractional integro-differential equation with a weakly singular kernel

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  • Qiao, Leijie
  • Xu, Da
  • Wang, Zhibo

Abstract

In this paper, we propose a fast and efficient numerical method to solve the two-dimensional integro-differential equation with a weakly singular kernel. The numerical method are considered by finite difference approach for spatial discretization and alternating direction implicit (ADI) method in time, combined with the second-order fractional quadrature convolution rule introduced by Lubich and the classical L1 approximation for Caputo fractional derivative. The detailed analysis shows that the proposed scheme is unconditionally stable and convergent with the convergence order O(τmin{1+α,2−α}+h12+h22). Some numerical results are also given to confirm our theoretical prediction.

Suggested Citation

  • Qiao, Leijie & Xu, Da & Wang, Zhibo, 2019. "An ADI difference scheme based on fractional trapezoidal rule for fractional integro-differential equation with a weakly singular kernel," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 103-114.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:103-114
    DOI: 10.1016/j.amc.2019.02.022
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    References listed on IDEAS

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    1. Xu, Da, 2017. "Numerical asymptotic stability for the integro-differential equations with the multi-term kernels," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 107-132.
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    Cited by:

    1. Qiao, Leijie & Xu, Da & Tang, Bo & Zhou, Jun, 2022. "Fast ADI difference/compact difference schemes for the nonlocal evolution equation with weakly singular kernels in three dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 329-347.
    2. Fang, Xing & Qiao, Leijie & Zhang, Fengyang & Sun, Fuming, 2023. "Explore deep network for a class of fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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