The rate of error growth in Hamiltonian-conserving integrators (Q1894289)

Hamiltonian-conserving numerical schemes are considered. It is shown that the rate of error-growth is at most linear in time when such methods are applied to problems whose period is uniquely determined by the value of the Hamiltonian. Pointing out that the rate of error growth for symplectic integrators is also asymptotically linear, the authors conclude that the Hamiltonian-conserving schemes are competitive in this respect. However, the relative merits of these two types of integrators should be judged from various aspects.