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A fully discrete θ-method for solving semi-linear reaction–diffusion equations with time-variable delay

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  • Tang, Changyang
  • Zhang, Chengjian

Abstract

In this paper, a fully discrete θ-method with 0≤θ≤1 is suggested to solve the initial–boundary value problem of semi-linear reaction–diffusion equations with time-variable delay. Under some appropriate conditions, a novel global stability criterion of the method is derived and it is shown that this method has the computational accuracy O(τ2+h2)(resp.O(τ+h2)) when θ=12(resp.θ≠12), where h and τ denote spatial and temporal stepsizes, respectively. Moreover, with some numerical experiments, the theoretical accuracy and global stability of the method are further illustrated.

Suggested Citation

  • Tang, Changyang & Zhang, Chengjian, 2021. "A fully discrete θ-method for solving semi-linear reaction–diffusion equations with time-variable delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 48-56.
    • Handle: RePEc:eee:matcom:v:179:y:2021:i:c:p:48-56
    DOI: 10.1016/j.matcom.2020.07.019
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    References listed on IDEAS

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    1. Wu, Fengyan & Li, Dongfang & Wen, Jinming & Duan, Jinqiao, 2018. "Stability and convergence of compact finite difference method for parabolic problems with delay," Applied Mathematics and Computation, Elsevier, vol. 322(C), pages 129-139.
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    Cited by:

    1. Jaradat, Imad & Alquran, Marwan & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2022. "Analytic simulation of the synergy of spatial-temporal memory indices with proportional time delay," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays," Mathematics, MDPI, vol. 11(3), pages 1-25, January.

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