Numerical oscillation and non-oscillation analysis of the mixed type impulsive differential equation with piecewise constant arguments
Numerical oscillation and non-oscillation analysis of the mixed type impulsive differential equation with piecewise constant arguments
复制标题
DOI：
10.1080/00207160.2023.2274277
复制
发表时间：
2023-10
影响因子：
1.8
通讯作者：
Zhaolin Yan;Jianfang Gao
中科院分区：
文献类型：
--
作者：
Zhaolin Yan;Jianfang Gao
本文的目的是研究具有分段常数参数的线性混合型脉冲微分方程的振荡和非振荡龙格-库塔方法。得到了数值解振荡和不振荡的条件。还得到了龙格-库塔方法能够保持分段常数参数的线性混合型脉冲微分方程的振荡和不振荡的条件。此外，还介绍了数值解的插值函数，并讨论了插值函数的性质。事实证明，插值函数的零点收敛到解析解的零点，其精度与相应的龙格-库塔方法的精度相同。为了证实理论结果，给出了数值例子。
The 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 are 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.