Stability analysis of linear multistep and Runge–Kutta methods for neutral multidelay-differential-algebraic systems

This paper is concerned with the stability analysis of linear multistep and Runge–Kutta methods for neutral multidelay-differential-algebraic systems. We focus on the system with no restrictive assumption on the structure of the coefficient matrices. It is shown that under some conditions, AA-stable linear multistep methods and AA-stable Runge–Kutta methods can preserve the delay-independent stability of the underlying linear systems. Numerical experiments further confirm the theoretical results.