Efficient symplectic algorithms for numerical simulations of Hamiltonian flows

A quite general approach to numerical simulations of Hamiltonian flows is presented, which is suitable to the development of efficient symplectic algorithms. Explicit schemes up to fourth order are worked out. These algorithms show a very good performance if implemented in typical molecular dynamics problems, i.e. in long-time simulations of Hamiltonian systems with a large number of degrees of freedom and steep potential functions.