Linear energy-preserving integrators for Poisson systems
David Cohen and Ernst Hairer
Abstract. For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge-Kutta method with infinitely many stages.
Key Words. Poisson system, energy preservation, Casimir function, partitioned Runge--Kutta method, collocation, Gaussian quadrature.