TY - JOUR
T1 - D-Convergence and Stability of a Class of Linear Multistep Methods for Nonlinear DDEs
AU - Zhang , Cheng-Jia
AU - Liao , Xiao-Xin
JO - Journal of Computational Mathematics
VL - 2
SP - 199
EP - 206
PY - 2000
DA - 2000/04
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9035.html
KW - D-Convergence, Stability, Multistep methods, Nonlinear DDEs.
AB - <p style="text-align: justify;">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 $D_{σγ}$, and a p-order linear multistep method together with a q-order Lagrangian interpolation leads to a D-convergent LMLM of order min {$p,q+1$}. &nbsp;</p>