NOUI Djaidja

Amrane Khaled

Approximate solution of Volterra integro differential equation by Euler polynomials

Gouadria Sara

On the numerical solution of Volterra -Fredholm integral equations

Nadir Mohamed Nasseh

On the Numerical solution of Volterra-Fredholmintegral equations using Tchebychev polynomials

GUERROUM Chaima

On the Numerical solution of Volterra-Fredholm integral equations using Taylor polynomials

HAIMED Amina

On the Numerical solution of mixed volterra- Fredholm integral equations

HAMMOU HIND

Comparison Between Touchard and Legendre Polynomials For Volterra Intégral Equations.

DIF Zeyneb

Sur des Equations Intégro-Différentielles

MADJIDI Imane

ON THE NUMERICAL SOLUTION OF VOLTERRA INTEGRAL EQUATIONS

TOUIL Randa

REGULARIZATION METHODS OF ILL POSED PROBLEMS

Mansour Mouchira

Approches par les splines et méthode Simpson modifiée des équations intégrales de Volterra de première espèce

Marouf Selma

Etude des certains problèmes mal-posés

Dilmi Nour el Houda

Résolution Numériques des équations integrales

Souyeh Siham

Décomposition en valeurs singuilières des problèmes mal posés

M'hamdia Rania

Solution approchée d'équations intégrales de Volterra de première espèce

Kebaili Nour el Imène

La méthode des moindres carrés pour les équations de la physique

As it is known the equation Aϕ = f with injective compact operator has a unique solution for all f in the range R(A).Unfortunately, the righthand side f is never known exactly, so we can take an approximate data fδ and used the perturbed problem αϕ + Aϕ = fδ where the solution ϕαδ depends continuously on the data fδ, and the bounded inverse operator (αI + A)−1 approximates the unbounded operator A−1 but not stable. In this work we obtain the convergence of the approximate solution of ϕαδ of the perturbed equation to the exact solution ϕ of initial equation provided α tends to zero with δ/√α. .

Citation

Noui DJAIDJA , Mostefa NADIR , , (2021), Comparison between Taylor and perturbed method for Volterra integral equation of the first kind, Numerical Algebra, Control and Optimization, Vol:11, Issue:4, pages:487-493, American Institute of Mathematical Sciences

Generally, when solving integral equations of the first kind, Tikhonov regularization is often used when the right-hand side of the equation is noisy. However, in this work, we propose a new regularization technique for solving Volterra integral equations of the first kind. Specifically, we have developed a method that is similar to Lavrentiev's classical method but tailored to the problem at hand. We have conducted a convergence analysis of our method and compared its performance to Tikhonov's method. Our results show that our proposed method outperforms Tikhonov's method for this specific problem. We provide several examples to illustrate the performance of our method. Overall, our work contributes to the field of numerical analysis by providing a new and effective method for solving Volterra integral equations of the first kind.

Citation

Noui DJAIDJA , ,(2021), Approximation Method For Volterra Integral Equation Of The First Kind.,1st International Conference on Pure and Applied Mathematics,IC-PAM’21, May 26-27, 2021, Ouargla, Algeria

Ce polycopié de cours, est un guide à la découverte des différentes fonctionnalités de base du logiciel Matlab. Matlab nous permet de résoudre numériquement de nombreux problèmes mathématiques. En outre, Matlab dispose de développement avec l’outil graphique. Le but de ce cours est de permettre aux étudiants de deuxième année licence mathématiques de : 1-Découvrir les bases du langage Matlab; 2-Apprendre la syntaxe de base du langage Matlab ; 3-Se familiariser rapidement avec Matlab ; 4-L’apprentissage de la programmation et des fonctionnalités principales de MATLAB.

Citation

NouiDJAIDJA , ,(2021); Notes de cours: outils de programmation 2,Université de Msila,

Generaly, to solve integral equation of the first kind must be use Tikhonov regularization when the free mumber of the equation is noised. In this work we present a convergence analysis for solving Volterra integral equation of the first kind by a new technical resemble to Lavrentiev classical method, where we find it better than Tikhonov's method. Some examples illustrate the performance of the this method.

Citation

Noui DJAIDJA , , (2018), Approximation Method for Volterra Integral Equation of the First Kind, Intrenational journal of mathematics and computation, Vol:29, Issue:4, pages:63-66, www.ceser.in/ceserp

In this work we introduce some essential spectra $(\sigma_{ei}, i=1,...,5)$ of a sequence of closed linear operators $(T_{n})_{n\in\mathbb{N}}$ on Banach space, we prove that if $(T_{n})_{n\in\mathbb{N}}$ converges in the generalized sense to a closed linear operator $T$, then there exists $n_{0}\in \mathbb{N}$ such that, for every $n\geq n_{0}$, we have $\sigma_{ei}(\lambda _{0}-(T_{n}+B))\subseteq \sigma _{ei}(\lambda_{0}-(T+B)), i=1,...,5$, where $B$ is a bounded linear operator, and $\lambda _{0}\in \mathbb{C}$. The same treatment is made when $(T_{n}-T)$ converges to zero compactly.

Citation

Noui DJAIDJA , , (2017), The Essential Spectrum of a Sequence of Linear Operators in Banach Spaces, International Journal of Analysis and Applications, Vol:15, Issue:1, pages:1-7, http://www.etamaths.com

Généralement la discrétisation d'une équation intégrale du première espèce conduira à un système linéaire mal conditionné.Une légère perturbation sur les données peut avoir une influence arbitrairement grande sur le résultat. Dans cet exposé nous utiliserons les méthodes de régularisation pour obtenir à une solution stable pour un système mal-conditionné.

Citation

Noui DJAIDJA , ,(2016), Sur les problèmes mal posés,Journées doctorales du laboratoire de mathématiques pures et appliquées,Université de M'sila