Runge-Kutta-Nystr\"om symplectic splitting methods of order 8
Numerical Analysis
2022-07-26 v2 Numerical Analysis
Abstract
Different families of Runge-Kutta-Nystr\"om (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.
Keywords
Cite
@article{arxiv.2202.01541,
title = {Runge-Kutta-Nystr\"om symplectic splitting methods of order 8},
author = {F. Casas and S. Blanes and A. Escorihuela-Tomàs},
journal= {arXiv preprint arXiv:2202.01541},
year = {2022}
}