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 differential 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 $A(\alpha)$-stability, and existing LMM codes can be used without any modification.

翻译：在这项工作中,我们研究运用古典理查森外推法加速线性多步法产生的序列趋同,以数字方式解决普通差别方程系统的初步价值问题,LMM-RE方法的优点是,综合法具有较高的顺序和有利的线性稳定性,其价值为$-或$-A(alpha)-stable,现有的LMM编码可以不作任何修改地使用。