  We extend the approach Abbott, Kedlaya and Roe to computation of the zeta
function of a projective hypersurface with $\tau$ isolated ordinary double
points over a finite field $\mathbb{F}_q$ given by the reduction of a
homogeneous polynomial $f \in \mathbb{Z}[x_0, \ldots, x_n]$, under the
assumption of equisingularity over $\mathbb{Z}_q$. The algorithm is based on
the results of Dimca and Saito (over the field $\mathbb{C}$ 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 $\mathbb{P}^3$.
