M. DJAIDJA Noui

MCA

Directory of teachers

Department

Mathematics Department

Research Interests

Integral equations Regularization of ill-posed problems Numerical Analysis

Contact Info

University of M'Sila, Algeria

Email : noui.djaidja@univ-msila.dz

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Recent Publications

2024-03-28

Approximate Solution of Linear Fredholm Integral Equation of the Second Kind Using Modified Simpson's Rule

In this paper, we introduce a novel approach to obtain approximate numerical solutions of linear Fredholm integral equations of the second kind. This method is founded on the modified Simpson's quadrature rule. We transform the Fredholm integral equation of the second kind into a system of linear equations and provide numerical examples. Numerical results were compared and interpreted with tables and graphs and the solution was shown to be consistent. Furthermore, we conduct a comparative analysis, comparing the absolute error in the solution with existed methods This comparison serves to highlight the efficiency and accuracy of our proposed method.
Citation

M. DJAIDJA Noui, (2024-03-28), "Approximate Solution of Linear Fredholm Integral Equation of the Second Kind Using Modified Simpson's Rule", [national] Mathematical Modelling of Engineering Problems , International Information and Engineering Technology Association

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2021

Notes de cours: outils de programmation 2

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

M. DJAIDJA Noui, (2021), "Notes de cours: outils de programmation 2", [national] Université de Msila

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Approximation Method For Volterra Integral Equation Of The First Kind.

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

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

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Comparison between Taylor and perturbed method for Volterra integral equation of the first kind

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.
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Citation

M. DJAIDJA Noui, (2021), "Comparison between Taylor and perturbed method for Volterra integral equation of the first kind", [national] Numerical Algebra, Control and Optimization , American Institute of Mathematical Sciences

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2018

Approximation Method for Volterra Integral Equation of the First Kind

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

M. DJAIDJA Noui, (2018), "Approximation Method for Volterra Integral Equation of the First Kind", [national] Intrenational journal of mathematics and computation , www.ceser.in/ceserp

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2017

The Essential Spectrum of a Sequence of Linear Operators in Banach Spaces

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

M. DJAIDJA Noui, (2017), "The Essential Spectrum of a Sequence of Linear Operators in Banach Spaces", [national] International Journal of Analysis and Applications , http://www.etamaths.com

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2016

Sur les problèmes mal posés

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

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

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