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Papers by Azedine Rahmoune

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

International Journal of Computer Mathematics

Research paper thumbnail of Solving Nonlinear Volterra-Fredholm Integral Equations using an Accurate Spectral Collocation Method

Tatra Mountains Mathematical Publications

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredho... more In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both L ∞ and weighted L 2 norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods.

Research paper thumbnail of Approximate solution of high-order integro-differential equations using radial basis functions

Journal of Applied Computer Science & Mathematics

Research paper thumbnail of Spectral collocation method for solving Fredholm integral equations on the half-line

Applied Mathematics and Computation, 2013

ABSTRACT The main purpose of this paper, is to present a spectral collocation method to approxima... more ABSTRACT The main purpose of this paper, is to present a spectral collocation method to approximate the solution of Fredholm integral equations of the second kind on the half-line. In this approach, interpolation operator based on scaled Laguerre functions is proposed. Also, convergence theorems are established under suitable assumptions. Finally, two numerical examples are presented and commented.

Research paper thumbnail of Solving Nonlinear Volterra-Fredholm Integral Equations Using an Accurate Spectral Collocation Method

Tatra Mountains Mathematical Publications, 2021

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredho... more In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both L∞ and weighted L2 norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods

Research paper thumbnail of Numerical solution of nonlinear Fredholm integro-differential equations using Chebyshev polynomials

Research paper thumbnail of The Australian Journal of Mathematical Analysis and Applications

As is well-known, underwater ridges and submerged horizontal cylinders can serve as waveguides fo... more As is well-known, underwater ridges and submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber in the direction of the ridge, there is only one trapped wave (this was proved in Bonnet & Joly (1993, SIAM J. Appl. Math.,53, pp. 1507–1550)). We construct the asymptotics of these trapped waves and their frequencies at high frequency by means of reducing the initial problem to a pair of boundary integral equations and then by applying the method of Zhevandrov & Merzon (2003, AMS Transl. (2),208, pp. 235–284), in order to solve them.

Research paper thumbnail of Sur la Résolution Numérique des ÉquationsIntégrales en utilisant des Fonctions Spéciales

Les equations integrales sont issues d’une maniere ou d’une autre a partir de plusieurs domaines ... more Les equations integrales sont issues d’une maniere ou d’une autre a partir de plusieurs domaines de la recherche scientifique, precisement par remaniement de certaines EDO et EDP ou naturellement par modelisation mathematique des differents problemes issus de la physique mathematique, de la biologie, de la chimie et des sciences de la technologie. Cependant, la resolution analytique de ces equations est pratiquement ardue, a savoir impossible dans la majore partie des cas. Cette these presente des methodes numeriques efficaces pour la resolution approchee des equations integrales dans un cadre fonctionnel, notamment, l’analyse de l’existence des solutions, l’etude de la convergence et l’estimation de l’erreur.

Research paper thumbnail of Approximate solution of high-order integro-differential equations using radial basis functions

Journal of Applied Computer Science & Mathematics, 2017

Research paper thumbnail of A rational spectral collocation method for solving Fredholm integral equations on the whole line

International Journal of Computing Science and Mathematics

Research paper thumbnail of Sinc-Nyström methods for Fredholm integral equations of the second kind over infinite intervals

Applied Numerical Mathematics

Research paper thumbnail of Efficient spectral-collocation methods for a class of linear Fredholm integro-differential equations on the half-line

Journal of Computational and Applied Mathematics

Research paper thumbnail of An efficient algorithm for solving Fredholm integral equations using piecewise quadratic interpolation

INTERNATIONAL JOURNAL OF ADVANCED SCIENTIFIC AND TECHNICAL RESEARCH

The main purpose of the present paper is to suggest a new simpler efficient algorithm based on pi... more The main purpose of the present paper is to suggest a new simpler efficient algorithm based on piecewise interpolation techniques for solving Fredholm integral equations by using quadratic polynomials with Newton's divided differences approach. The proposed method is consistent and remains non sensitive even when the number of knots increases. The convergence theorems have been established. Also, numerical results to illustrate the efficiency of the method are presented.

Research paper thumbnail of On the numerical solution of integral equations of the second kind with weakly singular kernels

... MA Abdou Department of Mathematics Faculty of Education Alexandria University Alexandria, Egy... more ... MA Abdou Department of Mathematics Faculty of Education Alexandria University Alexandria, Egypt Mohamed Abdalla Darwish Permanent address Mathematisches Seminar II Department of Mathematics Universität Kiel Faculty of Education D24098 Kiel, Deutschland ...

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

International Journal of Computer Mathematics

Research paper thumbnail of Solving Nonlinear Volterra-Fredholm Integral Equations using an Accurate Spectral Collocation Method

Tatra Mountains Mathematical Publications

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredho... more In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both L ∞ and weighted L 2 norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods.

Research paper thumbnail of Approximate solution of high-order integro-differential equations using radial basis functions

Journal of Applied Computer Science & Mathematics

Research paper thumbnail of Spectral collocation method for solving Fredholm integral equations on the half-line

Applied Mathematics and Computation, 2013

ABSTRACT The main purpose of this paper, is to present a spectral collocation method to approxima... more ABSTRACT The main purpose of this paper, is to present a spectral collocation method to approximate the solution of Fredholm integral equations of the second kind on the half-line. In this approach, interpolation operator based on scaled Laguerre functions is proposed. Also, convergence theorems are established under suitable assumptions. Finally, two numerical examples are presented and commented.

Research paper thumbnail of Solving Nonlinear Volterra-Fredholm Integral Equations Using an Accurate Spectral Collocation Method

Tatra Mountains Mathematical Publications, 2021

In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredho... more In this paper, we present a Jacobi spectral collocation method to solve nonlinear Volterra-Fredholm integral equations with smooth kernels. The main idea in this approach is to convert the original problem into an equivalent one through appropriate variable transformations so that the resulting equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. The convergence and error analysis are discussed for both L∞ and weighted L2 norms. We confirm the theoretical prediction of the exponential rate of convergence by the numerical results which are compared with well-known methods

Research paper thumbnail of Numerical solution of nonlinear Fredholm integro-differential equations using Chebyshev polynomials

Research paper thumbnail of The Australian Journal of Mathematical Analysis and Applications

As is well-known, underwater ridges and submerged horizontal cylinders can serve as waveguides fo... more As is well-known, underwater ridges and submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber in the direction of the ridge, there is only one trapped wave (this was proved in Bonnet & Joly (1993, SIAM J. Appl. Math.,53, pp. 1507–1550)). We construct the asymptotics of these trapped waves and their frequencies at high frequency by means of reducing the initial problem to a pair of boundary integral equations and then by applying the method of Zhevandrov & Merzon (2003, AMS Transl. (2),208, pp. 235–284), in order to solve them.

Research paper thumbnail of Sur la Résolution Numérique des ÉquationsIntégrales en utilisant des Fonctions Spéciales

Les equations integrales sont issues d’une maniere ou d’une autre a partir de plusieurs domaines ... more Les equations integrales sont issues d’une maniere ou d’une autre a partir de plusieurs domaines de la recherche scientifique, precisement par remaniement de certaines EDO et EDP ou naturellement par modelisation mathematique des differents problemes issus de la physique mathematique, de la biologie, de la chimie et des sciences de la technologie. Cependant, la resolution analytique de ces equations est pratiquement ardue, a savoir impossible dans la majore partie des cas. Cette these presente des methodes numeriques efficaces pour la resolution approchee des equations integrales dans un cadre fonctionnel, notamment, l’analyse de l’existence des solutions, l’etude de la convergence et l’estimation de l’erreur.

Research paper thumbnail of Approximate solution of high-order integro-differential equations using radial basis functions

Journal of Applied Computer Science & Mathematics, 2017

Research paper thumbnail of A rational spectral collocation method for solving Fredholm integral equations on the whole line

International Journal of Computing Science and Mathematics

Research paper thumbnail of Sinc-Nyström methods for Fredholm integral equations of the second kind over infinite intervals

Applied Numerical Mathematics

Research paper thumbnail of Efficient spectral-collocation methods for a class of linear Fredholm integro-differential equations on the half-line

Journal of Computational and Applied Mathematics

Research paper thumbnail of An efficient algorithm for solving Fredholm integral equations using piecewise quadratic interpolation

INTERNATIONAL JOURNAL OF ADVANCED SCIENTIFIC AND TECHNICAL RESEARCH

The main purpose of the present paper is to suggest a new simpler efficient algorithm based on pi... more The main purpose of the present paper is to suggest a new simpler efficient algorithm based on piecewise interpolation techniques for solving Fredholm integral equations by using quadratic polynomials with Newton's divided differences approach. The proposed method is consistent and remains non sensitive even when the number of knots increases. The convergence theorems have been established. Also, numerical results to illustrate the efficiency of the method are presented.

Research paper thumbnail of On the numerical solution of integral equations of the second kind with weakly singular kernels

... MA Abdou Department of Mathematics Faculty of Education Alexandria University Alexandria, Egy... more ... MA Abdou Department of Mathematics Faculty of Education Alexandria University Alexandria, Egypt Mohamed Abdalla Darwish Permanent address Mathematisches Seminar II Department of Mathematics Universität Kiel Faculty of Education D24098 Kiel, Deutschland ...