Numerical oscillation and non-oscillation analysis of the mixed type impulsive differential equation with piecewise constant arguments

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

International Journal of Computer Mathematics Pub Date : 2023-10-22 DOI:10.1080/00207160.2023.2274277

Zhaolin Yan, Jianfang Gao

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引用次数: 0

Abstract

AbstractThe purpose of this paper is to study oscillation and non-oscillation of Runge-Kutta methods for linear mixed type impulsive differential equations with piecewise constant arguments. The conditions for oscillation and non-oscillation of numerical solutions are obtained. Also conditions under which Runge-Kutta methods can preserve the oscillation and non-oscillation of linear mixed type impulsive differential equations with piecewise constant arguments are obtained. Moreover, the interpolation function of numerical solutions is introduced and the properties of the interpolation function is discussed. It turns out that the zeros of the interpolation function converge to ones of the analytic solution with the same order of accuracy as that of the corresponding Runge-Kutta method. To confirm the theoretical results, the numerical examples are given.Keywords: oscillationnumerical solutionRunge-Kutta methodsimpulsive delay differential equationspiecewise constant argumentsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.

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带分段常数参数的混合型脉冲微分方程的数值振动与非振动分析

摘要本文研究了具有分段常数参数的线性混合型脉冲微分方程的Runge-Kutta方法的振动性和非振动性。得到了数值解振荡和非振荡的条件。给出了龙格-库塔方法保持分段常参数线性混合型脉冲微分方程的振动性和非振动性的条件。引入了数值解的插值函数，并讨论了插值函数的性质。结果表明，插值函数的零点收敛于解析解的零点，其精度与相应的龙格-库塔方法的精度相同。为了验证理论结果，给出了数值算例。关键词:振荡，数值解，龙格-库塔方法，脉冲延迟微分方程，常数参数，免责声明作为对作者和研究人员的服务，我们提供了这个版本的接受稿件(AM)。在最终出版版本记录(VoR)之前，将对该手稿进行编辑、排版和审查。在制作和印前，可能会发现可能影响内容的错误，所有适用于期刊的法律免责声明也与这些版本有关。

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来源期刊

International Journal of Computer Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

5 months

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