(untitled) (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 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.