求解非线性中立型延迟微分方程一类线性多步方法的收敛性

CONVERGENCE OF A CLASS OF LINEAR MULTISTEP METHODS FOR NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

本文致力于带有Lagrang插值的一类线性多步法求解非线性中立型延迟微分方程的误差分析.证明了一个p′阶的线性多步方法配上一个q阶的Lagrang插值导致一个minf[p′,q+1]阶的E-(或EB-)收敛的非线性中立型延迟微分方程数值方法.

This paper is concerned with the error behavior of a class of linear multistep methods with the Lagrangian interpolation when applied to the nonlinear neutral delay differential equations （NDDEs）. It is shown that a p′- order linear multistep method together with a q- order Lagrangian interpolation leads to an E- （or EB-） convergent numerical method of order min{p′, q ＋ 1} for nonlinear NDDEs.