Singularity Subtraction for Nonlinear Weakly Singular Integral Equations of the Second Kind

Abstract

The singularity subtraction technique for computing an approximate solution of a linear weakly singular Fredholm integral equation of the second kind is generalized to the case of a nonlinear integral equation of the same kind. Convergence of the sequence of approximate solutions to the exact one is proved under mild standard hypotheses on the nonlinear factor, and on the sequence of quadrature rules used to build an approximate equation. A numerical example is provided with a Hammerstein operator to illustrate some practical aspects of effective computations.