一类自变量分段连续系统的振动性分析

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 826-838.

一类自变量分段连续系统的振动性分析

刘莹,高建芳*()

^{哈尔滨师范大学数学科学学院哈尔滨 150025}

收稿日期:2021-06-23 出版日期:2022-06-26 发布日期:2022-05-09
通讯作者: 高建芳 E-mail:09151108@163.com
基金资助:
国家自然科学基金(12001143);哈尔滨师范大学学术创新项目(HSDSSCX2020-33)

Oscillation Analysis of a Kind of Systems with Piecewise Continuous Arguments

Ying Liu,Jianfang Gao*()

^{School of Mathematical Sciences, Harbin Normal University, Harbin 150025}

Received:2021-06-23 Online:2022-06-26 Published:2022-05-09
Contact: Jianfang Gao E-mail:09151108@163.com
Supported by:
the NSFC(12001143);the Academic Innovation Project of Harbin Normal University(HSDSSCX2020-33)

摘要/Abstract

摘要：

该文主要运用$\theta$-方法对一类滞后型自变量分段连续系统的振动性进行分析，讨论了解析解和数值解的振动性和非振动性，得到了数值方法在解析解振动条件下保持方程振动性的充分条件，并给出了数值算例.

关键词: 自变量分段连续, 延迟微分系统, 数值解, 振动性, θ -方法

Abstract:

In this paper, we mainly use $\theta$-method to analyze the oscillation of differential equations with piecewise continuous arguments of retarded type, and discuss the oscillation and non-oscillation of analytic solution and numerical solution. The sufficient conditions for the numerical methods to preserve the oscillation of the equation under the condition of the analytic solution oscillation are obtained. Meanwhile, some numerical experiments are given.

Key words: Piecewise continuous arguments, Delay differential system, Numerical solutions, Oscillation, θ-methods

中图分类号:

O241.8

刘莹,高建芳. 一类自变量分段连续系统的振动性分析[J]. 数学物理学报, 2022, 42(3): 826-838.

Ying Liu,Jianfang Gao. Oscillation Analysis of a Kind of Systems with Piecewise Continuous Arguments[J]. Acta mathematica scientia,Series A, 2022, 42(3): 826-838.

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