Hamiltonian BVMs (HBVMs): A Family of “Drift Free” Methods for Integrating polynomial Hamiltonian problems

In this paper, we present a number of numerical results concerning the newly introduced class of Hamiltonian Boundary Value Methods (hereafter, HBVMs). Such methods are very suited for the numerical integration of Hamiltonian problems, since they are able to preserve, in the discrete solution, the exact value of polynomial Hamiltonians. In such a way, a numerical drift of the Hamiltonian, sometimes experienced when solving such problems, cannot occur. © 2009 American Institute of Physics