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Spherically symmetric (1D) black-hole spacetimes are considered as a test for numerical relativity. A finite difference code, based in the hyperbolic structure of Einstein's equations with the harmonic slicing condition is presented. Significant errors in the mass function are shown to arise from the steep gradient zone behind the black hole horizon, which challenge the Computational Fluid Dynamics numerical methods used in the code. The formalism is extended to moving numerical grids, whichdoi:10.1103/physrevd.51.1639 pmid:10018631 fatcat:xa47l4pqyfafpnrd5ozga4oake