Asymptotic Stability for Gauss Methods for Neutral Delay Differential Equations

Abstract

In [4] we proved that all Gauss methods are $N \tau (0)$-compatible for neutral delay differential equations (NDDEs) of the form:

where $a, b, c$ are real, $\tau ＞0, g(t)$ is a continuous real valued function. In this paper we are going to use the theory of order stars to characterize the asymptotic stability properties of Gauss methods for NDDEs. And then proved that all Gauss methods are $N\tau(0)-$stable.