  We have designed and tested a new relativistic Lagrangian hydrodynamics code,
which treats gravity in the conformally flat approximation to general
relativity. We have tested the resulting code extensively, finding that it
performs well for calculations of equilibrium single-star models, collapsing
relativistic dust clouds, and quasi-circular orbits of equilibrium solutions.
By adding in a radiation reaction treatment, we compute the full evolution of a
coalescing binary neutron star system. We find that the amount of mass ejected
from the system, much less than a percent, is greatly reduced by the inclusion
of relativistic gravitation. The gravity wave energy spectrum shows a clear
divergence away from the Newtonian point-mass form, consistent with the form
derived from relativistic quasi-equilibrium fluid sequences.
