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Numerical approximation of time fractional partial integro-differential equation based on compact finite difference scheme

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  • Luo, Ziyang
  • Zhang, Xingdong
  • Wang, Shuo
  • Yao, Lin

Abstract

In this paper, a new numerical scheme based on weighted and shifted Grünwald formula and compact difference operate is proposed. The proposed numerical scheme is used to solve time fractional partial integro-differential equation with a weakly singular kernel. Meanwhile the time fractional derivative is denoted by the Riemann-Liouville sense. Subsequently, we prove the stability and convergence of the mentioned numerical scheme and show that the numerical solution converges to the analytical solution with order O(τ2 + h4), where τ and h are time step size and space step size, respectively. The advantage is that the accuracy of the suggested schemes is not dependent on the fractional α. Furthermore, the numerical example shows that the method proposed in this paper is effective, and the calculation results are consistent with the theoretical analysis.

Suggested Citation

  • Luo, Ziyang & Zhang, Xingdong & Wang, Shuo & Yao, Lin, 2022. "Numerical approximation of time fractional partial integro-differential equation based on compact finite difference scheme," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922006051
    DOI: 10.1016/j.chaos.2022.112395
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    References listed on IDEAS

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    1. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 111-119.
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    3. Wang, Yanxin & Zhu, Li, 2016. "SCW method for solving the fractional integro-differential equations with a weakly singular kernel," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 72-80.
    4. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Kumar, Sunil & Kumar, Ajay & Samet, Bessem & Gómez-Aguilar, J.F. & Osman, M.S., 2020. "A chaos study of tumor and effector cells in fractional tumor-immune model for cancer treatment," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Zahrah I. Salman & Majid Tavassoli Kajani & Mohammed Sahib Mechee & Masoud Allame, 2023. "Fourth-Order Difference Scheme and a Matrix Transform Approach for Solving Fractional PDEs," Mathematics, MDPI, vol. 11(17), pages 1-15, September.
    2. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.

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