A note on the continuous-stage Runge-Kutta-(Nystr\"om) formulation of Hamiltonian Boundary Value Methods (HBVMs)

Abstract

In recent years, the class of energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) has been devised for numerically solving Hamiltonian problems. In this short note, we study their natural formulation as continuous-stage Runge-Kutta(-Nystr\"om) methods, which allows a deeper insight in the methods.