Energy-preserving variant of collocation methods
Ernst Hairer
Abstract. We propose a modification of collocation methods extending the `averaged vector field method' to high order. These new integrators exactly preserve energy for Hamiltonian systems, are of arbitrarily high order, and fall into the class of B-series integrators. We discuss their symmetry and conjugate-symplecticity, and we compare them to energy-preserving composition methods.
Key Words. Hamiltonian systems, energy-preserving integrators, B-series, Runge--Kutta methods, collocation, conjugate-symplecticity, symmetry, Gaussian quadrature.