  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.
