Geometric integration of conservative polynomial ODEs Original Research Article

We consider systems whose Hamiltonian is of the form View the MathML source, where the potential V is either cubic or quartic with no cubic terms. For most of these systems (in the measure sense) we give an explicit numerical integration method that preserves both phase space volume and the value of the Hamiltonian. This is exemplified in the Hénon–Heiles system. An application is to the hybrid Monte Carlo method of statistical mechanics, where the energy preservation means that steps are never rejected, allowing the time step to be increased and the autocorrelation decreased.