Functionally-fitted energy-preserving integrators for Poisson systems

TL;DR

This paper introduces a new class of high-order, energy-preserving integrators for Poisson systems using functionally-fitted technology, unifying and extending previous methods.

Contribution

It develops a novel approach for constructing energy-preserving integrators with arbitrarily high order for Poisson systems, building on and generalizing earlier methods.

Findings

Exact energy preservation achieved

Integrators can have arbitrarily high order

Conditions for unique solutions established

Abstract

In this paper, a new class of energy-preserving integrators is proposed and analysed for Poisson systems by using functionally-fitted technology. The integrators exactly preserve energy and have arbitrarily high order. It is shown that the proposed approach allows us to obtain the energy-preserving methods derived in BIT 51 (2011) by Cohen and Hairer and in J. Comput. Appl. Math. 236 (2012) by Brugnano et al. for Poisson systems. Furthermore, we study the sufficient conditions that ensure the existence of a unique solution and discuss the order of the new energy-preserving integrators.