Mathematics

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A COMPARISON OF NUMERICAL SOLUTIONS FOR ONE FREDHOLM INTEGRAL EQUATIONS SYSTEM OF THE SECOND KIND
(An-Najah National University, 2025-02-06) Badrien, Mohammed
The main goal of this work is to propose various numerical techniques for approximating the solution of a system of Fredholm integral equations of the second kind. The methods proposed involve the Chebyshev collocation method, the Haar wavelet method and the reconstruction of the variational iteration method. After reviewing the basic concepts of Fredholm integral equations and addressing the mathematical framework of these numerical methods, we provide some illustrative numerical examples with known exact solution to illustrate the effectiveness and the efficiency of these methods. Numerical results show clearly that Chebyshev collocation method is one of the most efficient method for solving system of Fredholm integral equations in comparison with its counterparts.