D-Convergence and Stability of a Class of Linear Multistep Methods for Nonlinear DDEs

Abstract

This paper deals with the error behaviour and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation (LMLMs) as applied to the nonlinear delay differential equations (DDEs). It is showtn that a LMLM is generally stable with respect to the problem of class $D_{\u03c3\u03b3}$, and a p-order linear multistep method together with a q-order Lagrangian interpolation leads to a D-convergent LMLM of order min {$p,q+1$}. \u00a0