D-CONVERGENCE AND STABILITY OF A CLASS OF LINEAR MULTISTEP METHODS FOR NONLINEAR DDES

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 shown that a LMLM is generally stable with respect to the problem of class D_σγ, and a p-order linear multistep method together with a q-order Lagrangian interpolation leads to a Dconvergent LMLM of order min{p, q + 1}.