Convergence, consistency and zero stability of impulsive one-step numerical methods

Gui-Lai Zhang

Applied Mathematics and Computation, 2022, vol. 423, issue C

Abstract: Impulsive one-step numerical methods are defined in the present paper, especially, a common and widely used numerical form generalised from Runge-Kutta methods defined as impulsive Runge-Kutta methods. And it is proved that a consistent and zero-stable method thus convergent. Moreover, it is also proved that an impulsive one-step numerical method is convergent of order p if the corresponding method is pth order. Another equivalent form of impulsive one-step numerical methods are also introduced. In addition, numerical experiments are provided to illustrate the advantage of impulsive Runge-Kutta methods.

Keywords: Impulsive Runge-Kutta method; Convergence; Consistency; Zero stability (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:423:y:2022:i:c:s0096300322001035

DOI: 10.1016/j.amc.2022.127017

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