In the context of damped second order linear dynamical systems, we study the asymptotic behavior of a time discretization of a slowly damped differential equation. We prove that this discretization can be constructed by means of a variable time step that gives rise to the same asymptotic behaviour as for the system in continuous time.

中文翻译：

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慢阻尼二阶动力系统自适应隐式离散化的渐近行为

在阻尼二阶线性动力系统的背景下，我们研究慢阻尼微分方程的时间离散化的渐近行为。我们证明这种离散化可以通过可变时间步长来构造，该时间步长会产生与连续时间系统相同的渐近行为。