  We present the numerical solution of the full gap equation in a weak coupling
constant $g$. It is found that the standard approximations to derive the gap
equation to the leading order of coupling constant are essential for a secure
numerical evaluation of the logarithmic singularity with a small coupling
constant. The approximate integral gap equation with a very small $g$ should be
inverted to a soft integral equation to smooth the logarithmic singularity near
the Fermi surface. The full gap equation is solved for a rather large coupling
constant $g\ge 2.0$. The approximate and soft integral gap equations are solved
for small $g$ values. When their solutions are extrapolated to larger $g$
values, they coincide the full gap equation solution near the Fermi surface.
Furthermore, the analytical solution matches the numerical one up to the order
one O(1). Our results confirm the previous estimates that the gap energy is of
the order tens to 100 MeV for the chemical potential $\mu\le 1000$ MeV. They
also support the validity of leading approximations applied to the full gap
equation to derive the soft integral gap equation and its analytical solution
near the Fermi surface.
