High order energy-preserving methods for Hamiltonian systems are presented. For this aim, an energy-preserving condition of continuous stage Runge--Kutta methods is proved. Order conditions are simplified and parallelizable conditions are also given. The computational cost of our high order methods is comparable to that of the average vector field method of order two.
@article{arxiv.1505.02537,
title = {A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems},
author = {Yuto Miyatake and John C. Butcher},
journal= {arXiv preprint arXiv:1505.02537},
year = {2016}
}