M. WALID Remili

MCB

Directory of teachers

Department

Mathematics Department

Research Interests

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

Contact Info

University of M'Sila, Algeria

Email : walid.remili@univ-msila.dz

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Recent Publications

2024-12-15

International Conference on Mathematics and its Applications in Science and Technology ICMAST'2024

This paper aims to solve a class of linear Fredholm integral equations on real line with underlying solutions decaying at in fnity by using the Galerkin method. Our approach is based upon mapped Gegenbauer rational functions. The properties of mapped Gegenbauer rational functions are utilized to convert the given Fredholm integral equations problems into a system of linear algebraic equations. Also, provide the error bound and the convergence rate of the presented method. Several selected numerical examples are
presented to show the performance and eciency of the proposed method.
1.
Citation

M. WALID Remili, (2024-12-15), "International Conference on Mathematics and its Applications in Science and Technology ICMAST'2024", [international] La présidente du premier Colloque International Sur les Mathématiques Appliquées et la Modélisation Mathématique , Setif 1 University Ferhat Abbas

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2024-11-12

Application of scaled Laguere collocation method into two-dimensional Fredholm integral equation in a semi-infinite domain

This paper presents a numerical solution for the two-dimensional Fredholm integral equation (TDFI) over a semi-infinite domain using the scaled Laguerre function
(SLF) collocation method. By transforming the TDFI into a system of linear algebraic equations, which are solved iteratively, the method’s efficiency and accuracy are
demonstrated through several numerical examples.
Citation

M. WALID Remili, (2024-11-12), "Application of scaled Laguere collocation method into two-dimensional Fredholm integral equation in a semi-infinite domain", [international] La présidente du premier Colloque International Sur les Mathématiques Appliquées et la Modélisation Mathématique , El Tarf

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2024-08-01

Mapped Gegenbauer functions for solving Hammerstein generalized integral equations with Green's kernels on the whole line

This paper introduces a collocation method for numerically solving Hammerstein generalized integral equations on the whole line. The approach utilizes mapped Gegenbauer functions to transform the Hammerstein integral equation into a system of nonlinear algebraic equations. Additionally, convergence results are obtained using the standard
L^2-norm. Finally, the effectiveness of the proposed method is demonstrated through several numerical experiments, which also serve to illustrate our theoretical findings.
Citation

M. WALID Remili, (2024-08-01), "Mapped Gegenbauer functions for solving Hammerstein generalized integral equations with Green's kernels on the whole line", [national] Journal of Computational and Applied Mathematics , Elsevier

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2024-01-10

Numerical solutions of nonlinear quadratic integral equations of Urysohn type on the half-line by using rational Legendre spectral method

A numerical method for solving nonlinear quadratic integral equations of Urysohn type on the half-line is presented. This approach reduces the given equation to a systematic procedure by using a rational Legendre-collocation approximation (RLC). The rate of convergence, error analysis and stability of the RLC method are investigated. Moreover, several numerical examples are carried out to verify the accuracy and reliability of the proposed method.
Citation

M. WALID Remili, (2024-01-10), "Numerical solutions of nonlinear quadratic integral equations of Urysohn type on the half-line by using rational Legendre spectral method", [national] Filomat , doiserbia.nb.rs

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2023-11-14

Galerkin spectral method for linear second‐kind Volterra integral equations with weakly singular kernels on large intervals

This paper considers the Galerkin spectral method for solving linear second-kind Volterra integral equations with weakly singular kernels on large intervals. By using some variable substitutions, we transform the mentioned equation into an equivalent semi-infinite integral equation with nonsingular kernel, so that the inner products from the Galerkin procedure could be evaluated by means of Gaussian quadrature based on scaled Laguerre polynomials. Furthermore, the error analysis is based on the Gamma function and provided in the weighted L2 -norm, which shows the spectral rate of convergence is attained. Moreover, several numerical experiments are presented to validate the theoretical results.
Citation

M. WALID Remili, (2023-11-14), "Galerkin spectral method for linear second‐kind Volterra integral equations with weakly singular kernels on large intervals", [national] Mathematical Methods in the Applied Sciences , Wiley Online Library}

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2023-10-06

Electromagnetic Scattering by Half-plane with Fractional Boundary Conditions Using Legendre Polynomials

The present study investigates a classical problem with different solution approaches. The E-polarized electromagnetic scattering by half-plane with fractional boundary conditions via two different methods is studied and the results are compared. The outcomes reveal that Legendre exponential functions are suitable as a complete set to express the induced current densities on the scatterer after several mathematical manipulations. The current and field distributions for different parameters are provided when the fractional order becomes 0.5 and 1.
Citation

M. WALID Remili, (2023-10-06), "Electromagnetic Scattering by Half-plane with Fractional Boundary Conditions Using Legendre Polynomials", [international] 2023 IEEE XXVIIIth International Seminar/Workshop Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED) , ukraine

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2023-09-26

A Matrix Mittag–Leffler Function and the Fractional Nonlinear Partial Integro-Differential Equation in ℝ^n

In this paper, we introduce the matrix Mittag–Leffler function, which is a generalization of the multivariate Mittag–Leffler function, in order to investigate the uniqueness of the solutions to a fractional nonlinear partial integro-differential equation in ℝ^𝑛 with a boundary condition based on Banach’s contractive principle and Babenko’s approach. In addition, we present an example demonstrating applications of the key results derived using a Python code that computes the approximate value of our matrix Mittag–Leffler function.
Citation

M. WALID Remili, (2023-09-26), "A Matrix Mittag–Leffler Function and the Fractional Nonlinear Partial Integro-Differential Equation in ℝ^n", [national] Fractal and Fractional , MDPI

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2022-02-17

Modified Legendre rational and exponential collocation methods for solving nonlinear Hammerstein integral equations on the semi-infinite domain

This paper discusses two efficient collocation methods for solving the Hammerstein integral equations on the semi-infinite domain, where the underlying solutions decay to zero at infinity. These methods are based upon modified Legendre rational and exponential functions, and reduce the Hammerstein integral equation to a nonlinear algebraic system. The error between the approximate and exact solutions in the usual L^2-norm is estimated. Finally, some numerical experiments are presented to examine and demonstrate the effectiveness and accuracy of the proposed methods in comparison to other approaches.
Citation

M. WALID Remili, (2022-02-17), "Modified Legendre rational and exponential collocation methods for solving nonlinear Hammerstein integral equations on the semi-infinite domain", [national] International Journal of Computer Mathematics , Taylor and Francis

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