Delay-Dependent Treatment of Linear Multistep Methods for Neutral Delay Differential Equations

Abstract

This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations $y'(t) = ay(t) + by(t - \tau) + cy'(t - \tau), t > 0, y(t) = g(t), -\tau ≤ t ≤ 0, a,b$  and $c \in  \mathbb{R}.$ The necessary condition for linear multistep methods to be $N_\tau(0)$-stable is given. It is shown that the trapezoidal rule is $N_\tau(0)$-compatible. Figures of stability region for some linear multistep methods are depicted.