We present a new numerical code for spherical hydrodynamics in general relativity. The code can handle gravitational collapse to a neutron star or to a black hole without the appearance of singularities. Moreover, the variables and equations in the code are very similar to those appearing in traditional Lagrangian supernova codes. Any such existing code can thus be easily adapted to treat collapse where the final fate is uncertain and may be either a neutron star or a black hole. The code is based on the formulation of Hernandez & Misner, in which retarded time is used as a coordinate. This prevents the computational grid from penetrating inside any black hole that may form. We present the equations and a complete finite difference scheme for the adiabatic evolution of a fluid that obeys a γ-law equation of state. We summarize the results of several test-bed calculations performed to check our code. We also give the transformation of the analytic Oppenheimer-Snyder solution for homogeneous dust collapse to our coordinate system.
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