This paper deals with asymptotic stability of differential-algebraic equations with multiple delays and numerical solutions generated by Runge–Kutta methods combined with Lagrange interpolation. We study the solvability and asymptotic stability of delay differential-algebraic equations and present some sufficient conditions for the zero solution to be asymptotically stable. A sufficient and necessary condition for the asymptotic stability of Runge–Kutta methods is provided. Further, some results on the asymptotic stability of high order Runge–Kutta methods are presented. Finally, two numerical examples are given to illustrate the numerical stability of the Runge–Kutta methods.

本文讨论了具有多重延迟的微分代数方程的渐近稳定性和由 Runge-Kutta 方法结合拉格朗日插值生成的数值解。我们研究了延迟微分代数方程的可解性和渐近稳定性，并提出了零解渐近稳定的一些充分条件。给出了龙格-库塔方法渐近稳定性的充分必要条件。此外，还介绍了一些关于高阶 Runge-Kutta 方法渐近稳定性的结果。最后，给出两个数值例子来说明龙格-库塔方法的数值稳定性。