Department of Mathematics

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Author: search.filters.author.Tahar Bechouat

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    Une variante de la méthode de Projection régularisée pour une classe d’équations intégrales de Fredholm de première espèce
    (HAL, 2022) Nadjib Boussetila; Tahar Bechouat
    Dans ce travail, on propose une procédure de régularisation et d’approximation numérique pour une classe d’équations intégrales de Fredholm de première espèce, basée sur la méthode LSQ projetée, où le sous-espace de projection est formé par les fonctions d’ondes sphéroïdales. Pour le paramètre de régularisation on adopte un choix a posteriori basé sur la méthode de Morozov cubique amortie. L’étude est justifiée par une analyse théorique détaillée (convergence, estimations d’erreur) sous certaines hypothèses de régularité imposées sur le noyau et les données du problème en question.
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    Exponential decay and numerical solution of nonlinear Bresse-Timoshenko system with second sound
    (Journal of Thermal Stresses, 2022) Salim Adjemi; Ahmed Berkane; Salah Zitouni; Tahar Bechouat
    This paper aims to study the one-dimensional nonlinear Bresse-Timoshenko system with second sound where the heat conduction given by Cattaneo’s law is effective in the second equation. We prove that the system is exponentially stable by using the energy method that requires constructing a suitable Lyapunov functional through exploiting the multipliers method. Furthermore, the result does not depend on any condition on the coefficients of the system. Finally, we validate our theoretical result by performing some numerical approximations based on the standard finite elements method, by using the backward Euler scheme for the temporal and spatial discretization.
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    A new class of nonlinear conjugate gradient coefficients for unconstrained optimization
    (Asian-European Journal of Mathematics, 2022) Amina Boumediene; Tahar Bechouat; Rachid Benzine; Ghania Hadji
    The nonlinear Conjugate gradient method (CGM) is a very effective way in solving largescale optimization problems. Zhang et al. proposed a new CG coefficient which is defined by BNPRPk . They proved the sufficient descent condition and the global convergence for nonconvex minimization in strong Wolfe line search. In this paper, we prove that this CG coefficient possesses sufficient descent conditions and global convergence properties under the exact line search.
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    New Method for Solving the Inverse Thermal Conduction Problem (Θ-Scheme Combined with CG Method under Strong Wolfe Line Search)
    (Buildings, 2023) Rachid Djeffal; Djemoui Lalmi; Sidi Mohammed El Amine Bekkouche; Tahar Bechouat; Zohir Younsi
    Most thermal researchers have solved thermal conduction problems (inverse or direct) using several different methods. These include the usual discretization methods, conventional and special estimation methods, in addition to simple synchronous gradient methods such as finite elements, including finite and special quantitative methods. Quantities found through the finite difference methods, i.e., explicit, implicit or Crank–Nicolson scheme method, have also been adopted. These methods offer many disadvantages, depending on the different cases; when the solutions converge, limited range stability conditions. Accordingly, in this paper, a new general outline of the thermal conduction phenomenon, called (θ-scheme), as well as a gradient conjugate method that includes strong Wolfe conditions has been used. This approach is the most useful, both because of its accuracy (16 decimal points of importance) and the speed of its solutions and convergence; by addressing unfavorable adverse problems and stability conditions, it can also have wide applications. In this paper, we applied two approaches for the control of the boundary conditions: constant and variable. The θ-scheme method has rarely been used in the thermal field, though it is unconditionally more stable for θ∈ [0.5, 1]. The simulation was carried out using Matlab software.
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    Numerical solution of the two-dimensional first kind Fredholm integral equations using a regularized collocation method
    (Computational and Applied Mathematics, 2023) Tahar Bechouat; Nadjib Boussetila
    In this study, we present an advanced numerical model for solving the 2D first kind Fredholm integral equations, which are well known to be ill-posed problems. This numerical approach is built on the quadrature formula with the Lavrentiev regularization method. Under some essential assumptions, a comprehensive theoretical explanation of the presented numerical approach is provided. Finally, various numerical examples support the theoretical findings and demonstrate the accuracy of our method.