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：我们探讨了求解微分代数方程组时的误差估计问题。理查森外推法是一种经典技术，可用于判断计算误差何时可忽略不计并估计离散化误差。我们使用GROMACS库对约束条件下的分子动力学进行了模拟，发现其输出并不总是适用于理查森外推法。我们通过多种数值实验推导并阐释了理查森外推法的应用。我们识别出两个必要条件，而GROMACS库并不总能满足这些条件。