La résolution numérique de quelques équations intégrales et intégro‐différentielles non linéaires par la méthode de collocation

Abstract

The main purpose of this thesis is to provide a direct, convergent and easy to implement numerical method to obtain the approximate solution for nonlinear Volterra integral equations and nonlinear Volterra integro-ifferential equations . Algorithms based on iterative collocation method is developed for the numerical solution of these kinds of equations. We also provide a rigorous error analysis. A theoretical proof is given and we present some numerical results which illustrate the performance of the methods