We consider the problem of estimating the error when solving a system of differential algebraic equations. Richardson extrapolation is a classical technique that can be used to judge when computational errors are irrelevant and estimate the discretization error. We have simulated molecular dynamics with constraints using the GROMACS library and found that the output is not always amenable to Richardson extrapolation. We derive and illustrate Richardson extrapolation using a variety of numerical experiments. We identify two necessary conditions that are not always satisfied by the GROMACS library.

翻译：本文探讨了求解微分代数方程组时的误差估计问题。Richardson外推法作为一种经典技术，可用于判断计算误差是否可忽略，并估计离散化误差。我们利用GROMACS库对含约束的分子动力学进行了模拟，发现输出结果并非总能适用Richardson外推法。通过一系列数值实验，我们推导并演示了Richardson外推法的应用，同时识别出GROMACS库中并非始终满足的两个必要条件。