  Singularity subtraction for linear weakly singular Fredholm integral
equations of the second kind is generalized to nonlinear integral equations.
Two approaches are presented: The Classical Approach discretizes the nonlinear
problem, and uses some finite dimensional linearization process to solve
numerically the discrete problem. Its convergence is proved under mild
hypotheses on the nonlinearity and the quadrature rule of the singularity
subtraction scheme. The New Approach is based on linearization of the problem
in its infinite dimensional setting, and discretization of the sequence of
linear problems by singularity subtraction. It is more efficient than the
former, as two numerical experiments confirm.
