(untitled) (Journal of Computational Mathematics, 2001)
This paper deals with the numerical solution of initial value problems for systems of neutral differential equations y'(t)=f(t,y(t),y(t- τ ),y'(t- τ )), t ＞ 0, y(t) = φ(t) t＜0, where τ＞ 0, f and φ denote given vector-valued functions. The numerical stability of a linear multistep method is investigated by analysing the solution of the test equations y'(t)=Ay(t) + By(t-τ) + Cy'(t-τ), where A, B and C denote constant complex N × N-matrices, and τ ＞ 0. We investigate the properties of adaptation of the linear multistep method and the characterization of the stability region. It is proved that the linear multistep method is NGP-stable if and only if it is A-stable for ordinary differential equations.