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 .
We integrate the three-dimensional Newtonian equations of hydrodynamics by the Riemann-solver based “ Piecewise Parabolic Method ” on an equidistant Cartesian grid .

Comparison ( a ) confronts the results of our grid-based PPM scheme with those from an SPH code .
We find that due to the lower numerical viscosity of the PPM code , the post-merging oscillations and pulsations can be followed for a longer time and lead to larger secondary and tertiary maxima of the gravitational wave luminosity and to a stronger peak of the gravitational wave spectrum at a frequency of about f \approx 1.8 KHz when compared to the results of Zhuge et al .
( 1994 ) .
In case ( b ) two grid based codes with the same backreaction formalism but differing hydrodynamic integrators and slightly different initial conditions are compared .
Instead of rotationally deformed initial neutron stars we use spherically shaped stars .
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 setting in when the two stars come very close .
In ( c ) we find that using a polytropic equation of state instead of the high-density equation of state of Lattimer & Swesty ( 1991 ) employed by Ruffert et al .
( 1996 ) does not change the overall dynamical evolution of the merger and yields agreement of the gravitational wave signature to within 20 % accuracy .
Whereas the polytropic law describes the dynamical behaviour of the bulk of the matter at and above nuclear density sufficiently well , we , however , find clear differences of the structure and evolution of the outer layers of the neutron stars where the stiffness of the equation of state is largely overestimated .
This has important implications for questions like mass loss and disk formation during the merging of binary neutron stars .