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Convergence and stability of compact finite difference method for nonlinear time fractional reaction–diffusion equations with delay

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  • Li, Lili
  • Zhou, Boya
  • Chen, Xiaoli
  • Wang, Zhiyong

Abstract

This paper is concerned with numerical solutions of nonlinear time fractional reaction–diffusion equations with time delay. A linearized compact finite difference scheme is proposed to solve the equations. In terms of a new developed fractional Gronwall type inequality, convergence and stability of the proposed scheme are obtained. Numerical experiments are given to illustrate the theoretical results.

Suggested Citation

  • Li, Lili & Zhou, Boya & Chen, Xiaoli & Wang, Zhiyong, 2018. "Convergence and stability of compact finite difference method for nonlinear time fractional reaction–diffusion equations with delay," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 144-152.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:144-152
    DOI: 10.1016/j.amc.2018.04.057
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    References listed on IDEAS

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    1. Hao, Zhaopeng & Fan, Kai & Cao, Wanrong & Sun, Zhizhong, 2016. "A finite difference scheme for semilinear space-fractional diffusion equations with time delay," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 238-254.
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    Cited by:

    1. Li, Lili & Zhao, Dan & She, Mianfu & Chen, Xiaoli, 2022. "On high order numerical schemes for fractional differential equations by block-by-block approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    2. Zhang, Qifeng & Ren, Yunzhu & Lin, Xiaoman & Xu, Yinghong, 2019. "Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 91-110.
    3. Hosseininia, M. & Heydari, M.H., 2019. "Legendre wavelets for the numerical solution of nonlinear variable-order time fractional 2D reaction-diffusion equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 400-407.
    4. A. S. Hendy & R. H. De Staelen, 2020. "Theoretical Analysis (Convergence and Stability) of a Difference Approximation for Multiterm Time Fractional Convection Diffusion-Wave Equations with Delay," Mathematics, MDPI, vol. 8(10), pages 1-20, October.
    5. Ahmed S. Hendy & Jorge E. Macías-Díaz, 2020. "A Discrete Grönwall Inequality and Energy Estimates in the Analysis of a Discrete Model for a Nonlinear Time-Fractional Heat Equation," Mathematics, MDPI, vol. 8(9), pages 1-15, September.

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