一类非线性延迟微分方程θ-方法的数值解振动分析  

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

作　　者：王云竹[1] 高建芳[1] Wang Yunzhu Gao Jianfang(School of Mathematical Sciences, 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

出　　处：《数学物理学报（A辑）》2017年第2期342-351,共10页Acta Mathematica Scientia

基　　金：黑龙江省自然科学基金(A201411;F2015012);国家自然科学基金(11401145)~~

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.This paper is concerned with oscillations of numerical solutions for a kind of non- linear 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 equa- tion. 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 numeri- cal experiments.

关 键 词：数值解 延迟微分方程 振动性 

分 类 号：O241.81[理学—计算数学]