Canonical Runge-Kutta methods (Q1122044)

An integration procedure is called canonical if it generates a globally canonical map if applied to a Hamiltonian system. In this note the author characterizes all canonical Runge-Kutta methods for Hamiltonian systems of the form \(\dot x=H^ T_ y\), \(\dot y=-H^ T_ x\) with Hamiltonian H(x,y,t), \(x,y\in {\mathbb{R}}^ n\), \(t\in {\mathbb{R}}\).