Solving non-differentiable Hammerstein integral equations via first-order divided differences

Abstract

[EN] In this paper, the behavior of derivative-free techniques to approximate solutions of nonlinear Hammerstein-type integral equations in Banach space C([alpha,beta]) as alternatives against the well-known Newton's method is examined. In particular, from the well-known Kurchatov method, we construct a uniparametric family of derivative-free iterative schemes in order to achieve an approximation of a solution of a Hammerstein-type integral equation with a non-differentiable Nemyskii operator. We compare the uniparametric family built and the Kurchatov method, obtaining improvements in the precision and also in the accessibility through studying its dynamic behavior.