Nonlinear Integral Equations of the Second Kind: A New Version of Nystrom Method

We consider the numerical approximation of a nonlinear integral operator equation by the Nystrom method. We propose a new way of applying this method which leads to a major improvement: We can theoretically attain any desired accuracy while for the classical Nystrom, the accuracy is limited by the quadrature error formula. The basic idea behind this new proposition is linearizing the nonlinear equation and discretizing the linearization process after, while the usual approach consists in the opposite.