Sur les équations intégo-différentielles et la méthode des éléments finis
Date
2025
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
university of bordj bou arreridj
Abstract
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.
Description
This 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.
Keywords
: Integro-differential equations, Lax-Milgram theorem, Finite element method, Lagrange, Interpolation
Citation
MD/37