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

Two Numerical Approaches for Nonlinear Weakly Singular Integral Equations