Traitement numérique par différence finie des équations intégro-différentielles avec retard

Abstract

n this thesis, we study a particular class of nonlinear Volterra integrodifferential equations with delay. Such equations are used to model dynamic phenomena that depend on the system’s history as well as a delayed term. We first recal the existence and uniqueness of the solution using the Picard iteration method. Then, we propose a numerical method based on backward finite differences, combined with a Nyström-type quadrature to handle the integral term. The analysis of the discrete system shows that the method is well-posed and convergent. Numerical simulations demonstrate the efficiency and accuracy of the proposed approach, confirming its relevance for solving this type of complex equation.