Linear multistep methods and Richardson extrapolation

In this talk, 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.
This is a joint work with Lajos Lóczi (ELTE Eötvös Loránd University, Hungary and BME Budapest University of Technology and Economics, Hungary). The main results are based on the paper \cite{FL2022} and on an ongoing research project.
{\bf Acknowledgments} The author was supported by the ÚNKP-22-5 New National Excellence Program of the Ministry for Culture and Innovation from the source of the National Research, Development and Innovation Fund.
\begin{thebibliography}{99} \bibitem{FL2022} \textsc{I. Fekete, L. Lóczi}, Linear multistep methods and global Richardson extrapolation, \textit{Appl. Math. Lett.}, \textbf{133}(2022), 108267. \end{thebibliography}