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Asymptotical stability of Runge–Kutta methods for advanced linear impulsive differential equations with piecewise constant arguments

Author

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  • Zhang, G.L.
  • Song, M.H.

Abstract

This paper is concerned with a class of advanced linear impulsive differential equations with piecewise continuous argument. The sufficient and necessary condition for asymptotical stability of the exact solution is obtained. Under this condition, asymptotical stability of Runge–Kutta methods for this kind of equations is studied. Some numerical examples are given to confirm the theoretical results.

Suggested Citation

  • Zhang, G.L. & Song, M.H., 2015. "Asymptotical stability of Runge–Kutta methods for advanced linear impulsive differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 831-837.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:831-837
    DOI: 10.1016/j.amc.2015.02.086
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    Cited by:

    1. Gui-Lai Zhang & Zhi-Yong Zhu & Yu-Chen Wang & Chao Liu, 2024. "Impulsive Discrete Runge–Kutta Methods and Impulsive Continuous Runge–Kutta Methods for Nonlinear Differential Equations with Delayed Impulses," Mathematics, MDPI, vol. 12(19), pages 1-30, September.
    2. 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.

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