  In this study, we perform full three dimensional numerical relativity
simulations of non-rotating general relativistic stars. Extending the studies
for polytropic equation of state, we investigate the accuracy and robustness of
numerical scheme on measuring fundamental ($f$)-mode frequency for realistic
equations of state (EoS). We use various EoS with varying range of stiffness
and numerically evolve perturbed stellar models for several mass configurations
(in the range of $1.2 - 2.0$ $M_{\odot}$) for each of these EoS. Using the
gravitational waveform obtained from the simulations we extract the $f$-modes
of the stars. The obtained results are tested against the pre-existing
perturbation methods and find good agreement. Validity and deviation of
universal relations have been carried out and are compared with earlier results
under Cowling approximation as well as perturbative approaches. We also show
that even using perturbed single star simulations can provide good agreement
with $f$-modes extracted from inspiral phase of binary neutron star simulations
which are computationally more expensive.
