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Asymptotical stability of numerical methods for semi-linear impulsive differential equations

  • Gui-Lai ZhangEmail author
Article
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Abstract

This paper is concerned with asymptotical stability of a class of semi-linear impulsive ordinary differential equations. First of all, sufficient conditions for asymptotical stability of the exact solutions of semi-linear impulsive differential equations are provided. Under the sufficient conditions, some explicit exponential Runge–Kutta methods can preserve asymptotically stability without additional restriction on stepsizes. Moreover, it is proved that some explicit Runge–Kutta methods can preserve asymptotical stability without additional restriction on stepsizes under stronger conditions.

Keywords

Impulsive differential equations Runge–Kutta method Exponential Runge–Kutta method Asymptotically stable 

Mathematics Subject Classification

65L05 65L06 65L07 65L20 

Notes

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsNortheastern University at QinhuangdaoQinhuangdaoPeople’s Republic of China

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