  We propose an efficient procedure for numerically evolving the Delta Kicked
Harmonic Oscillator. The method allows for longer and more accurate simulations
of the system as well as a simple procedure for calculating the systems Floquet
eigenstates and quasi-energies. The method is used to examine the dynamical
behaviour of the system in cases where the ratio of the kicking frequency to
the systems natural frequency is both rational and irrational.
