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

## TL;DR

This paper explores the continuous-stage Runge-Kutta(-Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs), providing deeper insight into their structure and properties for energy-conserving numerical solutions of Hamiltonian problems.

## Contribution

It introduces a continuous-stage formulation of HBVMs, enhancing understanding of their structure and potential advantages in solving Hamiltonian systems.

## Key findings

- Provides a new perspective on HBVMs as continuous-stage methods
- Deepens theoretical understanding of energy-conserving numerical methods
- Facilitates potential improvements in numerical algorithms for Hamiltonian problems

## 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.