M. KHIRANI Amina - Researcher Profile

Department

Mathematics Department

Research Interests

Specialized in Mathematics Department. Focused on academic and scientific development.

Contact Info

University of M'Sila, Algeria

Email : amina.khirani@univ-msila.dz

On the Web:

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Recent Publications

2025-04-06

Numerical solutions of Nonlinear Quadratic Volterra Integral Equations using Vieta-Lucas Wavelets

In this article, we present a numerical approach for solving Nonlinear Quadratic Volterra Integral Equations (NQVIEs) with the collocation method using Vieta-Lucas Wavelets (VLWs) and the Legendre Gauss Quadrature Rule (LGQR). First, we prove the existence and uniqueness of the main problem under specific conditions. Then, we apply the proposed method; the NQVIEs well be reduced to a system of nonlinear algebraic equations that can be solved by Newton’s method. We also estimate the error bound and the convergence of the presented method. Several numerical examples are mentioned in order to demonstrate its effectiveness and accuracy in solving NQVIEs.

Citation

M. KHIRANI Amina, (2025-04-06), "Numerical solutions of Nonlinear Quadratic Volterra Integral Equations using Vieta-Lucas Wavelets", [national] Applied Mathematics and Computational Mechanics , The Publishing Office of Czestochowa University of Technology

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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. KHIRANI Amina, (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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