  An implicit Lagrangian hydrodynamics code for general relativistic spherical
collapse is presented. This scheme is based on an approximate linearized
Riemann solver (Roe type scheme). This code is aimed especially at the
calculation of the late phase of collapse-driven supernovae and the nascent
neutron star, where there is a remarkable contrast between the dynamical time
scale of the proto-neutron star and the diffusion time scale of neutrinos,
without such severe limitation of the Courant condition at the center of the
neutron star. Several standard test calculations have been done. Two other
adiabatic simulations have also been done in order to test the performance of
the code in the context of the collapse-driven supernovae. It is found that the
time step can be extended far beyond the Courant limitation at the center of
the neutron star. The details of the scheme and the results of these test
calculations are discussed.
