  The effects of nonlinear oscillations in compact stars are attracting
considerable current interest. In order to study such phenomena in the
framework of fully nonlinear general relativity, highly accurate numerical
studies are required. We present a numerical scheme specifically tailored for
studies, based on formulating the time evolution in terms of deviations from a
stationary equilibrium configuration. Using this technique, we investigate
nonlinear effects associated with radial oscillations of neutron stars for a
wide range of amplitudes. In particular, we discuss mode coupling due to
nonlinear interactions, the occurrence of resonance phenomena, shock formation
near the stellar surface as well as the capacity of nonlinearities to stabilize
perturbatively unstable neutron star models.
