Runge-Kutta-Nystrom symplectic splitting methods of order 8

Different families of Runge-Kutta-Nystrom (RKN) symplectic splitting methods of order 8 are presented for second-order systems of ordinary differential equations and are tested on numerical examples. They show a better efficiency than state-of-the-art symmetric compositions of 2nd-order symmetric schemes and RKN splitting methods of orders 4 and 6 for medium to high accuracy. For some particular examples, they are even more efficient than extrapolation methods for high accuracies and integrations over relatively short time intervals. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

Different families of Runge-Kutta-Nystrom (RKN) symplectic splitting methods of order 8 are presented and tested for second-order systems of ordinary differential equations. They demonstrate better efficiency than state-of-the-art symmetric compositions of 2nd-order symmetric schemes and RKN splitting methods of orders 4 and 6, particularly for medium to high accuracy. In some specific examples, they are even more efficient than extrapolation methods for high accuracies and integrations over relatively short time intervals.