Journal Articles

Permanent URI for this collectionhttps://dspace.univ-soukahras.dz/handle/123456789/216

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    A Variant of Projection-Regularization Method for ill-posed linear operator equations
    (International Journal of Computational Methods, 2020-09-20) Bechouat Tahar; Boussetila Nadjib; Rebbani Faouzia
    In the present paper, we report on a strategy for computing the numerical approximate solution for a class of ill-posed operator equations in Hilbert spaces: Kf = g. This approach is a combination of Tikhonov regularization method and the finite rank approximation of K. Finally, numerical results are given to show the effectiveness of this method.
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    On the numerical solution of weakly singular integral equations of the first kind using a regularized projection method
    (International Journal of Computer Mathematics, 2024-05-28) Bechouat Tahar; Boussetila Nadjib
    This study investigates a numerical method based on the Jacobi–Gauss quadrature for solving Fredholm integral equations of the first kind with a weakly singular kernel by combining the Tikhonov regularization and projection methods. This numerical method reduces the solution of the weakly singular integral equations of the first kind to the solution of a linear system of algebraic equations. The theoretical analysis of the proposed technique is provided. Finally, several tests are presented to show the validity and efficiency of this approach.