Two Schemes of Impulsive Runge–Kutta Methods for Linear Differential Equations with Delayed Impulses

Gui-Lai Zhang () and Chao Liu
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Gui-Lai Zhang: College of Sciences, Northeastern University, Shenyang 110819, China
Chao Liu: College of Sciences, Northeastern University, Shenyang 110819, China

Mathematics, 2024, vol. 12, issue 13, 1-17

Abstract: In this paper, two different schemes of impulsive Runge–Kutta methods are constructed for a class of linear differential equations with delayed impulses. One scheme is convergent of order p if the corresponding Runge–Kutta method is p order. Another one in the general case is only convergent of order 1, but it is more concise and may suit for more complex differential equations with delayed impulses. Moreover, asymptotical stability conditions for the exact solution and numerical solutions are obtained, respectively. Finally, some numerical examples are provided to confirm the theoretical results.

Keywords: impulsive Runge–Kutta methods; impulsive ? methods; convergence; asymptotical stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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