一类非线性延迟微分方程θ-方法的数值解振动分析

数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 342-351.

一类非线性延迟微分方程θ-方法的数值解振动分析

王云竹, 高建芳

哈尔滨师范大学数学科学学院哈尔滨 150025

收稿日期:2016-07-12 修回日期:2016-10-24 出版日期:2017-04-26 发布日期:2017-04-26
通讯作者: 高建芳 E-mail:09151108@163.com
基金资助:
黑龙江省自然科学基金（A201411，F2015012）和国家自然科学基金（11401145）

Oscillation Analysis of Numerical Solutions in the θ-Methods for a Kind of Nonlinear Delay Differential Equation

Wang Yunzhu, Gao Jianfang

School of Mathematical Sciences, Harbin Normal University, Harbin 150025

Received:2016-07-12 Revised:2016-10-24 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the Natural Science Foundation of Heilongjiang Province (A201411, F2015012) and the NSFC (11401145)

摘要/Abstract

摘要： 该文考虑一类非线性延迟微分方程数值解的振动性.通过振动性的理论将这个非线性延迟微分方程的振动性转化为相应的线性延迟微分方程的振动性，再利用线性θ-方法的相关内容得到相应数值解的形式，从而得到数值解振动的条件以及非振动解的一些性质.为了更有力说明结果，最后给出了相应的算例.

关键词: 数值解, 延迟微分方程, 振动性

Abstract: This paper is concerned with oscillations of numerical solutions for a kind of nonlinear delay differential equation. According to the oscillatory theory, the oscillation of the nonlinear delay differential equation is transformed to that of the linear delay differential equation. The form of the numerical solution is obtained by using the linear θ-method. Some conditions under which the numerical solution is oscillatory are obtained and the properties of non-oscillatory numerical solutions are investigated. To verify results, the article gives numerical experiments.

Key words: Numerical solution, Delay differential equation, Oscillation

中图分类号:

O241.81

王云竹, 高建芳. 一类非线性延迟微分方程θ-方法的数值解振动分析[J]. 数学物理学报, 2017, 37(2): 342-351.

Wang Yunzhu, Gao Jianfang. Oscillation Analysis of Numerical Solutions in the θ-Methods for a Kind of Nonlinear Delay Differential Equation[J]. Acta mathematica scientia,Series A, 2017, 37(2): 342-351.

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