Two singularity subtraction schemes for a class of nonlinear weakly singular integral equations

Abstract

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 Ap proach 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 dis cretization of the sequence of linear problems by singularity subtraction. It is more efficient than the former, as two numerical experiments confirm.