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Impulsive continuous Runge–Kutta methods for impulsive delay differential equations

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  • Zhang, Gui-Lai
  • Song, Ming-Hui

Abstract

The classical continuous Runge–Kutta methods are widely applied to compute the numerical solutions of delay differential equations without impulsive perturbations. However, the classical continuous Runge–Kutta methods cannot be applied directly to impulsive delay differential equations, because the exact solutions of the impulsive delay differential equations are not continuous. In this paper, impulsive continuous Runge–Kutta methods are constructed for impulsive delay differential equations with the variable delay based on the theory of continuous Runge–Kutta methods, convergence of the constructed numerical methods is studied and some numerical examples are given to confirm the theoretical results.

Suggested Citation

  • Zhang, Gui-Lai & Song, Ming-Hui, 2019. "Impulsive continuous Runge–Kutta methods for impulsive delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 160-173.
    • Handle: RePEc:eee:apmaco:v:341:y:2019:i:c:p:160-173
    DOI: 10.1016/j.amc.2018.08.019
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    References listed on IDEAS

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    1. G. L. Zhang & M. H. Song & M. Z. Liu, 2012. "Asymptotic Stability of a Class of Impulsive Delay Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, October.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    3. Zhang, G.L. & Song, Minghui & Liu, M.Z., 2015. "Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 12-21.
    4. Zhang, Gui-Lai, 2017. "High order Runge–Kutta methods for impulsive delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 12-23.
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    Cited by:

    1. Gui-Lai Zhang & Chao Liu, 2024. "Two Schemes of Impulsive Runge–Kutta Methods for Linear Differential Equations with Delayed Impulses," Mathematics, MDPI, vol. 12(13), pages 1-17, July.
    2. Zhang, Gui-Lai, 2022. "Convergence, consistency and zero stability of impulsive one-step numerical methods," Applied Mathematics and Computation, Elsevier, vol. 423(C).

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