This paper studies fixed-step convergence of implicit-explicit general linear methods. We focus on a subclass of schemes that is internally consistent, has high stage order, and favorable stability properties. Classical, index-1 differential algebraic equation, and singular perturbation convergence analyses results are given. For all these problems IMEX GLMs from the class of interest converge with the full theoretical orders under general assumptions. The convergence results require the time steps to be sufficiently small, with upper bounds that are independent on the stiffness of the problem.

中文翻译：

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隐式-显式一般线性方法的收敛结果

本文研究了隐显一般线性方法的固定步长收敛。我们专注于内部一致、具有高阶阶和良好稳定性的方案子类。给出了经典的、index-1 微分代数方程和奇异摄动收敛分析结果。对于所有这些问题，来自感兴趣类别的 IMEX GLM 在一般假设下与完整的理论阶数收敛。收敛结果要求时间步长足够小，上限与问题的刚度无关。