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Now showing 1 - 5 of 8

Recent Submissions

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Numerical Analysis II
(University Hassiba Benbouali of Chlef, 2026) MEZOUAGHI Abdelheq
Numerical analysis forms the cornerstone of modern scientific computing, enabling the solution of complex mathematical problems where analytical methods fail. This discipline is crucial for physics simulations, engineering design, financial modeling, and artificial intelligence applications. Our course material equips second-year LMD mathematics students with fundamental computational techniques, beginning with linear system solutions (Gaussian elimination, iterative methods) in Chapter 1. Chapter 2 covers eigenvalue problems, essential for stability analysis and machine learning algorithms. First-order differential equations (Chapter 3) model dynamic systems in biology and economics, solved numerically via Euler and Runge-Kutta methods. The final chapter tackles nonlinear algebraic systems using Newton-Raphson iterations, vital for optimization and control theory. Through algorithmic rigor and MATLAB examples, we emphasize error analysis and computational efficiency. Progressive exercises develop both theoretical understanding and practical implementation skills, preparing students for research and industry challenges in applied mathematics.
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Numerical Analysis I
(University Hassiba Benbouali of Chlef, 2026) MEZOUAGHI Abdelheq
Numerical analysis is a fundamental branch of applied mathematics that focuses on the design, analysis, and implementation of algorithms to obtain approximate solutions to mathematical problems when exact solutions are difficult or impossible to determine. In a context where exact computation is often replaced by numerical values, a rigorous study of errors, stability, and the accuracy of the methods used becomes essential. This Numerical Analysis 1 course material, intended for second-year undergraduate (LMD) mathematics students, aims to provide the theoretical foundations and practical tools necessary to understand and master the basic methods of numerical computation. It is structured into five chapters, each addressing a key area of numerical analysis and supported by examples and exercises designed to encourage progressive learning. Chapter 1: Numerical Errors This chapter introduces the concepts of numerical errors, particularly truncation and rounding errors, decimal notation of approximated numbers, and absolute and relative error analysis. These notions are crucial for evaluating the reliability of numerical results. Chapter 2: Solving Algebraic Equations This chapter deals with the solution of algebraic equations, presenting iterative methods such as the bisection method, the fixed-point method, and the Newton-Raphson method, with particular attention paid to convergence and error estimation. Chapter 3: Interpolation and Approximation This chapter is dedicated to interpolation and approximation. It covers the Lagrange and Newton interpolation methods, the study of interpolation errors, and least-squares approximation techniques for fitting data. Chapter 4: Numerical Differentiation This chapter focuses on numerical differentiation, particularly useful when the function in question is only known through discrete data points. Chapter 5: Numerical Integration This chapter addresses numerical integration, discussing classical methods such as the rectangle rule, trapezoidal rule, and Simpson’s rule, with emphasis on their accuracy and applications. This educational resource seeks to combine mathematical rigor with the practical aspects of numerical computation, while fostering in students a critical approach to interpreting numerical results. It provides an essential introduction to numerical analysis and prepares students for more advanced modules in their mathematics curriculum.
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Carbon Dioxide Treatment Using Electrical Discharges
(Toufik TAHRI / Hocine TEBANI, 2026-04-28) Mohamed CHENOUI
This thesis investigates the application of non-thermal dielectric barrier discharge (DBD) plasma for the conversion of carbon dioxide (CO₂) at atmospheric pressure, with the objective of improving CO₂ activation and conversion efficiency under controlled operating conditions. Nonthermal plasmas offer a promising alternative to conventional thermal processes by enabling efficient energy transfer to electrons while maintaining low gas temperatures, thereby favoring selective chemical reactions. A self-consistent plasma model is developed to describe the electrical and physicochemical behavior of CO₂/Ar DBD discharges. The model accounts for electron kinetics, plasma chemistry, charge transport, and electric field evolution within the reactor.Particular attention is given to the role of gas composition and dielectric properties in shaping discharge dynamics and stability. The influence of key operating parameters, including applied voltage, excitation frequency, gas pressure, argon concentration, and dielectric material characteristics, is systematically analyzed through numerical simulations. The results demonstrate that the addition of argon significantly enhances electron density and promotes more stable discharge behavior by reducing the breakdown voltage and facilitating electron impact processes. Optimal CO₂ conversion performance is obtained at intermediate excitation frequencies and applied voltages, where a balance between discharge intensity and stability is achieved. In contrast, increasing the gas pressure leads to reduced conversion efficiency due to enhanced collisional losses and reduced electron mean free path. The simulated electrical characteristics and plasma behavior show good agreement with experimental observations, validating the reliability of the proposed model. Overall, this work provides valuable insights into the mechanisms governing CO₂ activation in DBD plasmas and highlights the importance of operating parameter optimization for the development of efficient plasma-based CO₂ conversion and environmental technologies.
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Global Existence of Small Data Solutions to Some Semi-linear σ-Evolution Models
(KAINANE MEZADEK Abdelatif / KAINANE MEZADEK Mohamed, 2026-06-04) SAIAH SEYYID ALI
In this thesis, we are interested to study Global existence of small data solutions to some semilinear σ-evolution models. The main goal of this study is to clarify the effect of the influence of parameters and the data onthe rang and qualitative properties of solutions. Using modified Bessel functions and the Mittag-Leffler function, we show some polynomial decay Lm − Lq estimates of Sobolev solutions to related linear models with vanishing right-hand side. We explain connections between the fractional orders and the exponents, which allow to prove the global (in time) existence of small-data Sobolev solutions by applying the fixed-point argument
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AI Techniques for Control and Observation of Nonlinear Dynamic Systems
(Souaad TAHRAOUI, 2026-05-19) AZEDDINE BELOUFA
This thesis confronts the gap between theory and practice in controlling the Twin Rotor MIMO System (TRMS). A conventional approach combining a backstepping controller with a fixed-gain High-Gain Observer (HGO) was first evaluated, demonstrating successful performance in simulation for both setpoint regulation and trajectory tracking. When transferred to the physical platform, the regulation performance was preserved, confirming the validity of the design under steady-state conditions. However, the same controller failed completely during real-time trajectory tracking, revealing a fundamental limitation of the fixed-gain observer architecture: its inability to simultaneously ensure fast state estimation and suppress real-world sensor noise under dynamic operating conditions. To resolve this specific failure mode, an adaptive control architecture was designed in which online-learning neural networks intelligently tune the observer gains in real time. Two distinct schemes were developed: a Feedforward Neural Network (FFNN) and a Radial Basis Function Neural Network (RBFNN), both modulating the HGO parameters based on the live observation error. Experimental validation on a TRMS testbed confirms that both proposed methods achieve robust and accurate tracking under the exact conditions that caused the conventional controller to fail. This work presents a proven solution to a documented real-world control problem and provides a direct comparative analysis of the FFNN and RBFNN approaches in this challenging application.