Energy conservation in modified Nyström methods for separable Hamiltonian systems

Abstract

Numerical integration methods that preserve structural properties of time dependent differential equations have often improved stability and smaller errors in long-term simulations than classical standard methods like Runge-Kutta or BDF. In the present paper an energy conserving Galerkin type approach of Betsch and Steinmann is generalized to modified Nyström methods for separable Hamiltonian systems. The benefits of this new class of methods are illustrated by numerical tests for a benchmark problem from celestial mechanics.