A derivation of energy-preserving exponentially-fitted integrators for Poisson systems

Exponentially-fitted (EF) methods are special methods for ordinary differential equations that better compute periodic/oscillatory solutions. Such solutions often appear in Hamiltonian systems, and in view of this, symplectic or energy-preserving variants of EF methods have been intensively studied recently. In these studies, the symplectic variants have been further applied to Poisson systems, while such a challenge has not ever been done for the energy-preserving variants. In this paper, we propose an energy-preserving EF method for Poisson systems, with special emphasis on the second- and fourth-order schemes.