  We study the effect of global error control in the numerical solution of
Hamiltonian systems. In particular, we apply the RKQ algorithm in the numerical
solution of a Hamiltonian system. This algorithm is designed to provide
stepwise control of both local and global error. A test problem demonstrates
the error control features of RKQ. Good results are obtained, despite the fact
that explicit Runge-Kutta methods have been used in RKQ, rather than symplectic
Runge-Kutta methods. This simply emphasizes the value of stepwise global error
control, as per the RKQ algorithm.
