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

作　　者：胡冰冰 高建芳[1,2] Bingbing Hu;Jianfang Gao(School of Mathematical Sciences,Harbin Normal University,Harbin 150025;Heilongjiang Key Laboratory of Analysis on Machine Learing and Dynamic System,Harbin Normal University,Harbin 150025)

机构地区：[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

出　　处：《数学物理学报(A辑)》2025年第1期203-213,共11页Acta Mathematica Scientia

基　　金：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)。

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θ-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.This article considers the oscillation of numerical solutions for a class of nonlinear delay differential equations with variable coefficients.By using the linearθ-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.

关 键 词：延迟微分方程 数值解 振动性 最终正解 

分 类 号：O241.8[理学—计算数学]