We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the pre-coalescing stage .
A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational .
The latter state is technically more complicated to treat than the former one ( synchronized binary ) , but is expected to represent fairly well the late evolutionary stages of a binary neutron star system .
As regards the gravitational field , an approximation of general relativity is used , which amounts to solving five of the ten Einstein equations ( conformally flat spatial metric ) .
The obtained system of partial differential equations is solved by means of a multi-domain spectral method .
Two spherical coordinate systems are introduced , one centered on each star ; this results in a precise description of the stellar interiors .
Thanks to the multi-domain approach , this high precision is extended to the strong field regions .
The computational domain covers the whole space so that exact boundary conditions are set to infinity .
Extensive tests of the numerical code are performed , including comparisons with recent analytical solutions .
Finally a constant baryon number sequence ( evolutionary sequence ) is presented in details for a polytropic equation of state with \gamma = 2 .