Delay-Dependent Treatment of Linear Multistep Methods for Neutral Delay Differential Equations (Journal of Computational Mathematics, 2003)
This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations $y'(t) = ay(t) + by(t - τ) + cy'(t - τ), t > 0, y(t) = g(t), -τ ≤ t ≤ 0, a,b$ and $c \in \mathbb{R}.$ The necessary condition for linear multistep methods to be $N_τ(0)$-stable is given. It is shown that the trapezoidal rule is $N_τ(0)$-compatible. Figures of stability region for some linear multistep methods are depicted.
Keywords: Delay-dependent stability; Linear multistep methods; Neutral delay differential equations.