一类具有变系数的非线性延迟微分方程数值解的振动性分析

一类具有变系数的非线性延迟微分方程数值解的振动性分析

Oscillation Analysis of Numerical Solutions for a Class of Nonlinear Delay Differential Equations with Variable Coefficients

摘要/Abstract

图/表 2

参考文献 24

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 203-213.

胡冰冰¹(),高建芳^1,^2,^*()

¹哈尔滨师范大学数学科学学院哈尔滨 150025
²哈尔滨师范大学黑龙江省机器学习与动态系统分析重点实验室哈尔滨 150025

收稿日期:2023-05-22 修回日期:2024-06-06 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: * 高建芳,E-mail:09151108@163.com
作者简介:胡冰冰,E-mail:2836522449@qq.com
基金资助:
黑龙江省机器学习与动态系统分析重点实验室开放研究基金(HLJKL2505)

Bingbing Hu¹(),Jianfang Gao^1,^2,^*()

¹School of Mathematical Sciences, Harbin Normal University, Harbin 150025
²Heilongjiang Key Laboratory of Analysis on Machine Learing and Dynamic System, Harbin Normal University, Harbin 150025

Received:2023-05-22 Revised:2024-06-06 Online:2025-02-26 Published:2025-01-08
Supported by:
Open Research Fund of Heilongjiang Key Laboratory of Analysis on Machine Learning and Dynamic System(HLJKL2505)

摘要：

该文主要考虑了一类具有变系数的非线性延迟微分方程数值解的振动性, 运用线性 $\theta$ -方法和线性化理论, 将非线性差分方程的振动性转化为其对应的线性化方程的振动性, 运用不等式比较和放缩技巧, 得到了数值解振动的条件.

关键词: 延迟微分方程, 数值解, 振动性, 最终正解

Abstract:

This article considers the oscillation of numerical solutions for a class of nonlinear delay differential equations with variable coefficients. By using the linear $\theta$ -methods and linearization theory, the oscillation of the nonlinear difference equation is transformed into that of its corresponding linearized equation. By using inequality comparisons and scaling techniques, the conditions of the oscillation for the numerical solutions are obtained.

Key words: delay differential equation, numerical solutions, oscillation, eventually positive solution

中图分类号:

O241.8

胡冰冰, 高建芳. 一类具有变系数的非线性延迟微分方程数值解的振动性分析[J]. 数学物理学报, 2025, 45(1): 203-213.

Bingbing Hu, Jianfang Gao. Oscillation Analysis of Numerical Solutions for a Class of Nonlinear Delay Differential Equations with Variable Coefficients[J]. Acta mathematica scientia,Series A, 2025, 45(1): 203-213.

图1

方程 (3.1) 的数值解, $\theta=0.8, h=0.05$ "

图1

图2

方程 (3.2) 的数值解, $\theta=0.2, h=0.025$ "

图2

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