In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary diffe- rential equations numerically. The advantage of the LMM-RE approach is that the combined method possesses higher order and favorable linear stability properties in terms of $A$- or $A\left(\alpha \right)$-stability, and existing LMM codes can be used without any modification.

中文翻译：

---

线性多步法和全局理查森外推

在这项工作中，我们研究了经典 Richardson 外推 (RE) 技术的应用，以加速由线性多步方法 (LMM) 产生的序列收敛，以数值求解常微分方程系统的初值问题。LMM-RE 方法的优点是组合方法在以下方面具有更高阶和良好的线性稳定性特性$\mathrm{一个}$- 或者$\mathrm{一个}\left(\alpha \right)$- 稳定性，现有的 LMM 代码无需任何修改即可使用。