Zeta functions of projective hypersurfaces with ordinary double points

We extend the approach of Abbott, Kedlaya and Roe to computation of the zeta function of a projective hypersurface with tau isolated ordinary double points over a finite field F-q given by the reduction of a homogeneous polynomial f is an element of Z[x(0), ..., x(n)], under the assumption of equisingularity over Z(q). The algorithm is based on the results of Dimca and Saito (over the field C of complex numbers) on the pole order spectral sequence in the case of ordinary double points. We give some examples of explicit computations for surfaces in P-3.