二阶时滞微分方程周期解的存在唯一性及数值解法

Existence and Uniqueness of Periodic Solution to Second-order Delay Differential Equations with a Numerical Solution Method

证明了二阶时滞微分方程的周期解存在唯一的一个充分条件,讨论了其周期解的数值解法:利用数值微分和线性插值对微分方程进行离散,得到非线性方程组,再用牛顿法求解;最后给出了实例,说明了方法的有效性.

In this paper,a sufficient condition for existence and uniqueness of periodic solution to second-order delay differential equations is proved and numerical solution of its periodic solution is discussed.Numerical differential and linear interpolation are used to discretize the differential equation and linear equations set is obtained,then Newton method is used for the solution.Finally,an example illustrates the effectiveness of the method.