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Asymptotical stability of the exact solutions and the numerical solutions for impulsive neutral differential equations

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Abstract

In this paper, we not only study asymptotical stability of a class of linear impulsive neutral delay differential equations(INDDEs), but also study stability and asymptotical stability of nonlinear INDDEs. Asymptotical stability of zero solution of linear INDDEs is studied by the properties of simple autonomous linear neutral delay differential equations(NDDEs) without impulsive perturbations. Base on this idea, numerical methods of INDDEs are constructed. The constructed numerical methods preserve asymptotical stability of linear INDDEs if corresponding methods are A-stable. Moreover, some stability and asymptotical stability criteria are established for nonlinear INDDEs, respectively. The constructed numerical methods which can preserve stability and asymptotical stability of the exact solutions under these criteria are obtained. Some numerical examples are given to confirm the theoretical results.

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Data Availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. College of sciences, Northeastern University, Shenyang, 110819, China

    Gui-Lai Zhang, Yang Sun & Zhi-Wei Wang

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  1. Gui-Lai Zhang
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  2. Yang Sun
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  3. Zhi-Wei Wang
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Correspondence to Gui-Lai Zhang.

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Communicated by Hui Liang.

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This work is supported by the NSF of PR China (No. 11701074).

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Zhang, GL., Sun, Y. & Wang, ZW. Asymptotical stability of the exact solutions and the numerical solutions for impulsive neutral differential equations. Comp. Appl. Math. 43, 8 (2024). https://doi.org/10.1007/s40314-023-02518-0

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  • DOI: https://doi.org/10.1007/s40314-023-02518-0

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