  We implement the numerical method of summing Green function diagrams on the
Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our
method has previously been applied to the attractive Hubbard model for low
density. Here we apply our numerical algorithm to the Hubbard model close to
half filling ($\rho = 0.40$), and for $T/t = 0.03$, in order to study the
dynamics of one- and two-particle Green functions. For the values of the chosen
parameters we see the formation of three branches which we associate with the a
two-peak structure in the imaginary part of the self-energy. From the imaginary
part of the self-energy we conclude that our system is a Fermi liquid (for the
temperature investigated here), since Im$\Sigma(\vec{k},\omega) \approx w^2$
around the chemical potential. We have compared our fully self-consistent FLEX
solutions with a lower order approximation where the internal Green functions
are approximated by free Green functions. These two approches, i.e., the fully
selfconsistent and the non-selfconsistent ones give different results for the
parameters considered here. However, they have similar global results for small
densities.
