  In this paper we design discrete port-Hamiltonian systems systematically in
two different ways, by applying discrete gradient methods and splitting methods
respectively. The discrete port-Hamiltonian systems we get satisfy a discrete
notion of passivity, which lets us, by choosing the input appropriately, make
them globally asymptotically stable with respect to an equilibrium point. We
test methods designed using the discrete gradient approach in numerical
experiments, and the results are encouraging when compared to relevant existing
integrators of identical order.
