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中文摘要：
1 引言 中立型微分方程广泛出现于生物学、物理学及工程技术等诸多领域．数值求解中立型微分方程时，数值方法的稳定性研究具有无容置疑的重要性，其中渐近稳定性的研究是其重要组成部分．对于线性中立型延迟微分方程，渐近稳定性研究已有许多重要结果，如文献[1，2，3，4，5，6]等．对于非线性中立型变延迟微分方程，
英文摘要：
In this paper, we consider a class of linear multistep methods for nonlinear neutral differential equations with variable delay, which possesses proportional guarantee of the asymptotic stability of the theoretical solutions. The numerical solution obtained by this class of methods with appropriate approximations to delay term and neutral term is asymptotically stable.
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