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A new set of equations and a new numerical method for computing stationary axisymmetric rapidly rotating star models within general relativity is presented. The source term of the gravitational field is not restricted to a perfect fluid one but represents the most general one, including anisotropic stresses, permitted under the assumptions of stationarity, axisymmetry and absence of meridional currents. This allows us to derive the equations governing the equilibrium of rotating neutron stars with strong magnetic fields in a self-consistent and fully relativistic way. As regards the numerics, the improvement lies in the exact computation of the metric in the whole space outside the star, thanks to a numerical grid which extends to infinity (due to a suitable compactification of the space external to the star). The numerical integration is performed by means of an iterative procedure based on a spectral method, which provides results far more precise than previous methods, with "evanescent" numerical errors. The code efficiency is demonstrated by considering a simple polytropic equation of state, this paper being not intended to present new astrophysical results but the equations governing more general objects than previously considered (for instance magnetized neutron starts) and the numerical method to integrate them. In that spirit, a particular emphasis is given to the evaulation of the numerical errors. A certain integral quantity is shown to be a very good indicator of the discrepancy between the numerical solution and the exact one.
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