中文摘要：

隐显线性多步方法由隐式线性多步方法和显式线性多步法组合而成．本文主要讨论求解满足单边Lipschitz条件的非线性刚性初值问题和一类奇异摄动初值问题的隐显线性多步方法的误差分析．最后，由数值例子验证了所获的理论结果的正确性及方法处理这两类问题的有效性。

英文摘要：

Implicit-explicit linear multistep methods are composed of implicit linear multistep methods and explicit linear multistep methods. In this paper, we are focused on error analysis of the implicit-explicit linear multistep methods for the nonlinear stiff initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems. Numerical examples verify the validity of the obtained theoretical results and the effectiveness of the implicit-explicit linear multistep methods.