  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.
