ZERAIBI Khalissa2025-07-132025MD/37MD/37https://dspace.univ-bba.dz/handle/123456789/334This part concludes the thesis by giving an assessment of the work carried out and the possible perspectives. The main goal of this work was to construct numerical methods for some integral, integro-differential and differential equations. We applied numerical methods such as: the finite deference method, the finite element method and Gauss Legendre quadra ture. These methods consist of looking for solutions in the form of a linear combination of the elements of the base. A considerable contribution has been made in this work for the numerical solution of integro-differential equations, using the finite element method. Considering the different tables given, we can affirm the effectiveness of this approach. This work can be extended to other types of integral and integro-differential equations.The main objective of this thesis is to propose a theoretical and numerical study on lin ear integro-differential equations. we used Lax Milgram theorems to provide existence and uniqueness results for linear integro-differentials. In addition, we applied the finite element method for the approximate solution of some linear integro-differential equations. Finally, several numerical examples are given to show the effectiveness of our approaches.en: Integro-differential equationsLax-Milgram theoremFinite element methodLagrangeInterpolationThesis