Linear multistep methods and global Richardson extrapolation

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.