Master

Solutions périodiques d'une équation de Riccati généralisée

2025-10-28T07:52:33Z

Solutions périodiques d'une équation de Riccati généralisée TOUAILIA, LINA The intention of this memoir is to analyze the relationship between the dynamics of limit cycles in planar di¤erential systems ( _ x = P (x; y) _ y = Q (x; y)) and the analytical properties of generalized Riccati equations. It will attempt, using a qualitative and transformational approach, to analyze how some representations of the Riccati equation could predict or describe the existence of limit cycles in non-linear systems.

Solutions périodiques de certaines classes d'équations différentielles perturbées

2025-10-28T07:48:34Z

Solutions périodiques de certaines classes d'équations différentielles perturbées TALBI, Hana In this work, we consider the limit cycles of a class of polynomial differential systems of the form {┊ u=v-ε(g₁¹(u)+f₁¹(u)v)-ε²(g₁²(u)+f₁²(u)v), v=-u-ε(g₂¹(u)+f₂¹(u)v)-ε²(g₂²(u)+f₂²(u)v), where g₁¹,g₁²,f₁¹,f₁²,g₂¹,g₂²,f_{2 }¹and f₂² are polynomials of a given degree and ε is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of a linear center u=v, v=-u, by using the averaging theory of first and second order. This work addresses a special case of the second part of Hilbert's 16th problem, which remains unsolved in general. The results contribute to the qualitative understanding of perturbed planar polynomial systems.

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

2025-10-28T07:45:31Z

Traitement numérique par différence finie des équations intégro-différentielles avec retard BELHIRECHE, Nor el houda 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.

Shooting method for boundary value problems in ordinary differential equations

2025-10-28T07:43:01Z

Shooting method for boundary value problems in ordinary differential equations BENABDELHAFID, BOUTHEYNA This study employs the one-dimensional shooting method to numerically solve a boundary value problem (BVP) governed by an ordinary differential equation (ODE). Such BVPs arise in diverse scientific and engineering domains, including thermal conduction, semiconductor physics, electrochemistry, heat transfer, elasticity, thermoelasticity, plasma physics, materials with memory effects, and population dynamics