  We present an approximation scheme to solve the Non Perturbative
Renormalization Group equations and obtain the full momentum dependence of the
$n$-point functions. It is based on an iterative procedure where, in a first
step, an initial ansatz for the $n$-point functions is constructed by solving
approximate flow equations derived from well motivated approximations. These
approximations exploit the derivative expansion and the decoupling of high
momentum modes. The method is applied to the O($N$) model. In leading order,
the self energy is already accurate both in the perturbative and the scaling
regimes. A stringent test is provided by the calculation of the shift $\Delta
T_c$ in the transition temperature of the weakly repulsive Bose gas, a quantity
which is particularly sensitive to all momentum scales. The leading order
result is in agreement with lattice calculations, albeit with a theoretical
uncertainty of about 25%.
