A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems

TL;DR

This paper develops high-order energy-preserving numerical methods for Hamiltonian systems, providing simplified conditions for their construction, parallelization strategies, and demonstrating their computational efficiency comparable to existing methods.

Contribution

It introduces a new energy-preserving condition for continuous stage Runge-Kutta methods, simplifies order conditions, and offers parallelizable strategies for high-order Hamiltonian system integration.

Findings

Energy-preserving condition proved for continuous stage Runge-Kutta methods

Simplified order conditions facilitate method construction

Computational cost comparable to second-order average vector field method

Abstract

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.