Stability and numerical analysis for delay differential equations

利用这一结果，我们得到了一些与泛函微分方程有关的结果。首先，我们给出了一类时滞差分方程解的全局稳定性条件。其次，我们给出了具有比例延迟的延迟微分方程和Volterra积分方程解的配置方法的可达阶。超级可达到的订单也被考虑在内。最后，我们考虑了具有时滞的传染病模型的全局稳定性。利用显式格式和隐式格式相结合的离散化方法，得到了一类具有时滞的离散化SIRS传染病模型的全局动力学解，与连续模型的解相对应。

We obtained some results related to the functional differential equations by this grant. We first derived new global stability conditions for a class of difference equations with time delay. Next, we showed an attainable order of collocation methods for delay differential and Volterra integral equations with proportional delay. Super attainable order was also considered. Finally, we considered some global stability for epidemic models with time delay. Using a discretization of combined explicit with implicit schemes, we obtained the global dynamics of a discretized SIRS epidemic model with time delay, corresponding to that of continuous model.