中立型延迟微分方程的Euler-方法的数值振动性(英文)

Numerical oscillations of the Euler method for neutral delay differential equations

讨论了中立型延迟微分方程ddt(y(t)+py(t-τ))+qy(t)=0的Euler-方法的数值振动性。把显式Euler方法和隐式Euler方法分别应用到这个中立型微分方程,得到了两个关于数值解的差分方程。利用差分方程的所有解振动等价于其特征方程没有正根这一重要结论,得到了这两个差分方程所有解振动的充分条件,从而得到了差分方程振动的充分条件。

Numerical oscillations of the Euler method for a neutral delay differential equation d/dt（y（t） ＋py（t -τ） ） ＋ qy（t） = 0 are discussed. By applying the explicit and implicit Euler methods to the neutral delay differential equation, two difference equations of the numerical solution are obtained. Based on the important conclusion that all solutions of the difference equation oscillate if and only if its corresponding characteristic equation has no positive roots, the sufficient conditions under which every so- lution of the two difference equations oscillates are investigated, and then the sufficient conditions under which difference equations oscillate are obtained.