Functionally-fitted energy-preserving integrators for Poisson systems
For researchers in geometric numerical integration, this provides a unified framework for high-order energy-preserving integrators for Poisson systems, though it is an incremental extension of known methods.
This paper proposes a new class of energy-preserving integrators for Poisson systems using functionally-fitted technology, achieving exact energy conservation and arbitrarily high order. The methods generalize existing approaches by Cohen and Hairer (2011) and Brugnano et al. (2012).
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.