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An implicit Lagrangian hydrodynamics code for general relativistic sphericalcollapse is presented. This scheme is based on an approximate linearizedRiemann solver (Roe type scheme). This code is aimed especially at thecalculation of the late phase of collapse-driven supernovae and the nascentneutron star, where there is a remarkable contrast between the dynamical timescale of the proto-neutron star and the diffusion time scale of neutrinos,without such severe limitation of the Courant condition at the center of theneutron star. Several standard test calculations have been done. Two otheradiabatic simulations have also been done in order to test the performance ofthe code in the context of the collapse-driven supernovae. It is found that thetime step can be extended far beyond the Courant limitation at the center ofthe neutron star. The details of the scheme and the results of these testcalculations are discussed.Comment: AASTeX v4.0, 24 pages, 13 figures on request from  shoichi@MPA-Garching.MPG.DE, submitted to Ap

An Implicit Lagrangian Code for Spherically Symmetric General Relativistic Hydrodynamics with an Approximate Riemann Solver