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High order Runge–Kutta methods for impulsive delay differential equations

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  • Zhang, Gui-Lai

Abstract

The purpose of this paper is to obtain high order Runge–Kutta methods for nonlinear impulsive delay differential equations (IDDEs). In order to achieve the purpose, continuity and smoothness of the exact solutions of IDDEs are analyzed. And then the discontinuous points and non-smooth points are chosen as a part of the nodes of the Runge–Kutta methods. Furthermore, it is proved that the pth order Runge–Kutta method for IDDEs is also convergent of order p. And some simple numerical examples are given to demonstrate the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:313:y:2017:i:c:p:12-23
    DOI: 10.1016/j.amc.2017.05.054
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. 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.

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