Extrapolation methods for the numerical solution of nonlinear Urysohn integral equations : a study on univariate and bivariate domain

In their recent article, Brezinski and Redivo-Zaglia propose a new competitive approach to solve a special subclass of nonlinear Fredholm integral equations of the second kind, called Urysohn integral equations in one variable. In their paper they focus on the exemplification of the performance of simplified topological epsilon-algorithm applied to the underlying system of nonlinear equations generated by the Nystrom Method in order to accelerate the convergence. In this thesis we want to present the results of my research that has allowed us to understand the underlying theoretical and empirical aspects. The performances obtained through our considerations are better than those originally published. A novelty that we propose in this thesis is the extension of this technique to the study of Urysohn integral equation defined on bivariate domain.