  Several applications of spectral methods to problems related to the
relativistic astrophysics of compact objects are presented. Based on a proper
definition of the analytical properties of regular tensorial functions we have
developed a spectral method in a general sphericallike coordinate system. The
applications include the investigation of spherically symmetric neutron star
collapse as well as the solution of the coupled 2D-Einstein-Maxwell equations
for magnetized, rapidly rotating neutron stars. In both cases the resulting
codes are efficient and give results typically several orders of magnitude more
accurate than equivalent codes based on finite difference schemes. We further
report the current status of a 3D-code aiming at the simulation of
non-axisymmetric neutron star collapse where we have chosen a tensor based
numerical scheme.
