  High resolution, non-oscillatory, central difference (NOCD) numerical schemes
are introduced as alternatives to more traditional artificial viscosity (AV)
and Godunov methods for solving the fully general relativistic hydrodynamics
equations. These new approaches provide the advantages of Godunov methods in
capturing ultra-relativistic flows without the cost and complication of Riemann
solvers, and the advantages of AV methods in their speed, ease of
implementation, and general applicability without explicitly using artificial
viscosity for shock capturing. Shock tube, wall shock, and dust accretion
tests, all with adiabatic equations of state, are presented and compared
against equivalent solutions from both AV and Godunov based codes. In the
process we address the accuracy of time-explicit NOCD and AV methods over a
wide range of Lorentz factors.
