  The dynamics, time evolution of the mass distribution, and gravitational wave
signature of coalescing neutron stars described by polytropes are compared with
three simulations published previously: (a) ``Run 2'' of Zhuge et al. (1994),
(b) ``Model III'' of Shibata et al. (1992), and (c) ``Model A64'' of Ruffert et
al. (1996). We aim at studying the differences due to the use of different
numerical methods, different implementations of the gravitational wave
backreaction, and different equations of state. Comparison (a) confronts the
results of our grid-based PPM scheme with those from an SPH code. We found that
due to the lower numerical viscosity of the PPM code, the post-merging
oscillations and pulsations could be followed for a longer time and lead to
larger secondary and tertiary maxima of the gravitational wave luminosity. In
case (b) two grid based codes with the same backreaction formalism but
differing hydrodynamic integrators and different numerical resolution are
compared. Satisfactory agreement of the amplitude of the gravitational wave
luminosity is established, although due to the different initial conditions a
small time delay develops in the onset of the dynamical instability. In (c) we
find that using a polytropic equation of state instead of the high-density
equation of state of Lattimer & Swesty (1991) does not change the overall
dynamical evolution of the merger and yields agreement of the gravitational
wave signature to within 20% accuracy. However, differences of the structure
and evolution of the outer layers of the neutron stars are present, which has
important implications for questions like mass loss and disk formation during
the merging of binary neutron stars.
