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

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Abstract

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, A-stable linear multistep methods and A-stable Runge–Kutta methods can preserve the delay-independent stability of the underlying linear systems. Numerical experiments further confirm the theoretical results.

Keywords

Asymptotic stability
Neutral multidelay-differential-algebraic systems
Linear multistep methods
Runge–Kutta methods

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This project is supported by NSFC (No. 10871078) and 863 Program of China (No. 2009AA044501).