Highly accurate calculation of rotating neutron stars - Detailed description of the numerical methods

We give a detailed description of the recently developed multi-domain spectral method for constructing highly accurate generalrelativistic models of rapidly rotating stars. For both "ordinary" and "critical" configurations, we show using representative examples, how the accuracy improves as the order of the approximation increases. As well as homogeneous fluid bodies, we also discuss models of polytropic and strange stars.