  We describe a numerical method for calculating the (3+1) dimensional general
relativistic hydrodynamics of a coalescing neutron-star binary system. The
relativistic field equations are solved at each time slice with a spatial
3-metric chosen to be conformally flat. Against this solution to the general
relativistic field equations the hydrodynamic variables and gravitational
radiation are allowed to respond. The gravitational radiation signal is derived
via a multipole expansion of the metric perturbation to the hexadecapole order
including both mass and current moments and a correction for the slow motion
approximation. Using this expansion, the effect of gravitational radiation on
the system evolution can also be recovered by introducing an acceleration term
in the matter evolution.
