ABDELKRIM Merzougui

Azouz Soria

Résolution numérique des équations intégrales de Volterra de secondes espèces par les fonctions splines polynomiales et non polynomiales

Rezig Safia

Résolution numérique des équations intégrales et integro-differentielles en utilisant les polynômes de Jacobi

Laiadi Abdelkader

Sur quelques problèmes d’écoulements à surfaces libres avec tension de surface

Zouaza Zinelabiddine , Ben farhat Elamin

Une comparaison de deux méthodes de projection pour la résolution des systèmes d’équations intégrales et intégro-différentielles de Fredholm et de Volterra

Adjimi Lobna

Traitement numériques des équations différentielles d’ordre fractionnel

Adjimi Lobna

Traitement numériques des équations différentielles d’ordre fractionnel

Ahmedbey Zineb , Benzaoui Imane

Sur quelques méthodes numériques pour la résolution des équations integro-différentilles

Seraidi berrachid

Résolution numérique des équations integro-différentilles via les polynômes d’Hermite

Zouareg Yahia

Résolution Numérique des équations intégrales de Fredholm en utilisant les polynômes de Chebychev

Chettouh Abir

Solution approchée des équations intégrales linéaires de Fredholm en utilisant les polynômes de Bernstein

Mihoune Nasrine

Résolution numériques des équations aux dérivées partielles par différence finies

Alouache Khaoula

Les méthodes numériques pour la résolution des équations différentielles ordinaires

Negeuz manel

Quelques méthodes de résolution numérique des équations integro- différentilles

Roubache samia

Sur quelques méthodes de résolution numériques des équations intégrales

Bouchama Kawther

Résolution numérique des différentes classes d’équations aux dérivées partielles par différences finies

Laiadi Abdelkader

Effet de la tension de surface sur des écoulements au-dessus des obstacles

Boudaoud Sarra

Applications de la méthode de simplexe aux problèmes d'économie

Oulha El Mahdi

Etude d'un problème d'écoulement au-dessus d'un creux triangulaire

In this paper, we provide an accurate numerical solution for space-time fractional linear diffusion equation involving the fractinal Caputo-Hadamard derivative. To do so, we have used a finite difference method. The Convergence and stability of the given finite difference scheme are studied using the mathematical induction technique. Moreover, Numerical examples are given to demonstrate the effectiveness of our results.

Citation

KAOUTHER Bouchama , YACINE Arioua , Abdelkrim MERZOUGUI , , (2023), Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative, International Journal of Applied and Computational Mathematics, Vol:9, Issue:4, pages:52, Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The main objective of this paper is to find accurate solutions for linear fractional differential equations involving the fractional Caputo-Hadamard derivative of order α > 0. Therefore, to achieve this objective, a new method called the Finite Fractional Difference Method (FFDM) is employed to find the numerical solution. As such, the convergence and stability of the numerical scheme is discussed and illustrated by solving two linear fractional differential equation problems of order 0 < α<=1 to show the validity of our method.

Citation

KAOUTHER Bouchama , Abdelkrim MERZOUGUI , YACINE Arioua , ADMIN Admin , , (2022), Numerical solutions for linear fractional differential equation with dependence on the Caputo-Hadamard derivative using finite difference method, Palestine Journal of Mathematics, Vol:11, Issue:, pages:28-36, Nouressadat Touafek

In this paper, a numerical approximation solution of a space-time fractional diffusion equation (FDE), involving Caputo-Katugampola fractional derivative is considered. Stability and convergence of the proposed scheme are discussed using mathematical induction. Finally, the proposed method is validated through numerical simulation results of different examples.

Citation

KAOUTHER Bouchama , YACINE Arioua , Abdelkrim MERZOUGUI , , (2022), The numerical solution of the space-time fractional diffusion equation involving the Caputo-Katugampola fractional derivative, Numerical Algebra, Control and Optimization, Vol:12, Issue:3, pages:621-636, Bulent Karasozen

The objective of this present work is to study various approaches to the numerical solution of fractional partial differential equations (FPDEs) of the Caputo-Katugampola type. Among the intriguing methods explored in our study, we emphasize the Adomian Decomposition Method (ADM), the Homotopy Perturbation Method (HPM), and the Iterative Decomposition Method (IDM).

Citation

KAOUTHER Bouchama , Abdelkrim MERZOUGUI , YACINE Arioua , ,(2019-11-21), Fractional Differential Equations of Caputo- Katugampola Type and numerical Solutions,RAMA 11,Sidi Bel Abbès

The problem of steady two-dimensional flow of a fluid of finite depth over a successive obstacles is considered. Both gravity and surface tension are taken into account in the dynamic boundary conditions. The fluid is assumed to be inviscid, incompressible and the flow to be irrotational. The flow is characterized by the two parameters, the Froude number Fr and the inverse Weber number δ. The fully non-linear problem is solved numerically by using the boundary integral equation technique. The numerical solutions for sub-critical (Fr < 1) and supercritical (Fr > 1) are presented for various values of Fr and δ. The effects of surface tension and gravity on the shape of the free surface are discussed, and solution diagrams for all flow regimes are presented.

Citation

Abdelkrim MERZOUGUI , Abdelkader Laiadi, , (2019), Free surface flows over a successive obstacles with surface tension and gravity effects, AIMS Mathematics Journal, Vol:4, Issue:2, pages:316-326, AIMS Press

Two-dimensional free-surface flows of an inviscid and incompressible fluid over multiple obstacles is considered. The flow is assumed to be steady and irrotational. Both gravity and surface tension are included in the dynamic boundary conditions. Far upstream, the flow is assumed to be uniform. Multiples obstructions are located at the channel bottom. In this paper, the fully nonlinear problem is formulated by using a boundary integral equation technique. The resulting integro-differential equations are solved iteratively by Newton’s method. When surface tension and gravity are included, there are two additional parameters in the problem known as the Weber number and Froude number. Finally, solution diagrams for all flow regimes are presented.

Citation

Abdelkrim MERZOUGUI , ABDELKADER LAIAD, , (2018), NUMERICAL SOLUTION FOR A FREE SURFACE FLOW OVER MULTIPLE OBSTACLES, Electronic Journal of Mathematical Analysis and Applications (EJMAA), Vol:6, Issue:1, pages:266-275, EJMAA

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x''(t) + p(t)x'(t) + q(t)x(t) =r(t)x'(t-thau(t)) = f (t; x (t) ; x(t-thau(t))) + c(t)x(t-thau(t)); is considered. By employing Green's function and Krasnoselskii's fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order delay differential equation.

Citation

Abdelkrim MERZOUGUI , FARID NOUIOUA, ABDELOUAHEB ARDJOUNI, , (2017), EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR A THIRD-ORDER DELAY DIFFERENTIAL EQUATION, International Journal of Analysis and Applications, Vol:13, Issue:2, pages:136-143, IJAA

Effect of surface tension and gravity on a free surface flow over two trapezoidal obstacles

Citation

Abdelkrim MERZOUGUI , ,(2017), Effect of surface tension and gravity on a free surface flow over two trapezoidal obstacles,International Conference on Applied Analysis and Mathematical Modeling (ICAAMM 2017),Istanbul GeliŞim University, Istanbul, Turkey

Free-surface flow over a triangular obstacle is considered. The fluid is assumed to be inviscid, incompressible and the flow is assumed to be steady and irrotational. Both gravity and surface tension are included in the dynamic boundary condition. Far upstream, the flow is assumed to be uniform. The problem is solved numerically using a boundary integral equation method. The problem is solved by first deriving integro-differential equations. These equations are discretized and the resulting nonlinear algebraic equations are solved by Newton method. When surface tension and gravity are included, there are two additional parameters in the problem known as the Weber number and Froude number.

Citation

Abdelkrim MERZOUGUI , Abdelkader. Laiadi, , (2016), Non Linear Free-Surface Flow Over a Submerged Obstacle, General Letters in Mathematics(GLM), Vol:1, Issue:1, pages:45-52, REFAAD

Numerical solution for a free surface flow under an inclined gate with the effect of surface tension and gravity

Citation

Abdelkrim MERZOUGUI , ,(2016), Numerical solution for a free surface flow under an inclined gate with the effect of surface tension and gravity,International Arab Conference on Mathematics and Computations IACMC 2016,Zarqa University, Jordan

Free-Surface Flow under a gate with gravity and surface tension effect

Citation

Abdelkrim MERZOUGUI , ,(2016), Free-Surface Flow under a gate with gravity and surface tension effect,International Congress on Fundamental and Applied Sciences ICFAS 2016,YIDIZ TECHNICAL UNIVERSITY ISTANBUL, TURKEY

Approximate solution for linear Fredholm integral equation by using Bernstein polynomials

Citation

Abdelkrim MERZOUGUI , ,(2016), Approximate solution for linear Fredholm integral equation by using Bernstein polynomials,3eme Congrès de de la société mathématiques Algérienne,Batna university

Numerical of free surface flow under gate

Citation

Abdelkrim MERZOUGUI , ,(2015), Numerical of free surface flow under gate,Journées doctorales 2015, Université de M’sila,M'sila university

Two-dimensional steady free-surface flows over an obstacle is considered. The fluid is assumed to be inviscid, incompressible and the flow is irrotational. Both gravity and surface tension are included in the dynamic boundary conditions. Far upstream, the flow is assumed to be uniform. Triangular obstruction is located at the channel bottom. In this paper, the fully nonlinear problem is formulated by using a boundary integral equation technique. The resulting integro-differential equations are solved iteratively by using Newton’s method. When surface tension and gravity are included, there are two additional parameters in the problem known as the Weber number and Froude number. Finally, solution diagrams for all flow regimes are presented.

Citation

Abdelkrim MERZOUGUI , Abdelkader Laiadi, , (2014), FREE SURFACE FLOW OVER A TRIANGULAR DEPRESSION, TWMS J. App. Eng. Math., Vol:4, Issue:1, pages:67-73, FEYZİYE SCHOOLS FOUNDATION IŞIK UNIVERSITY Faculty of Arts and Sciences

Numerical solution for free surface flow over multiple Obstacles

Citation

Abdelkrim MERZOUGUI , ,(2014), Numerical solution for free surface flow over multiple Obstacles,International Arab Conference on Mathematics and Computations IACMC 2014,Zarqa University, Jordan

Free-Surface Flow over Triangular Obstacle

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Abdelkrim MERZOUGUI , ,(2014), Free-Surface Flow over Triangular Obstacle,International Arab Conference on Mathematics and Computations IACMC 2014,Zarqa University, Jordan

Free-Surface Flow over Triangular Obstacle

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Abdelkrim MERZOUGUI , ,(2013), Free-Surface Flow over Triangular Obstacle,9th International Symposium on Geometric Function Theory and Applications,IŞIK University, Istanbul, TURKEY

Free-Surface Flow over a step

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Abdelkrim MERZOUGUI , ,(2012), Free-Surface Flow over a step,The Fourth International Conference on Mathematical Sciences ICM2012,Al-Ain United Arab Emirates University

Surface tension effect on a two-dimensional channel flow against an inclined wall is considered. The flow is assumed to be steady, irrotational, inviscid and incompressible. The effect of surface tension is taken into account and the effect of gravity is neglected. Numerical solutions are obtained via series truncation procedure. The problem is solved numerically for various values of the Weber number α and for various values of the inclination angle β between the horizontal bottom and the inclined wall

Citation

Abdelkrim MERZOUGUI , ,(2011), A waveless Two-Dimentional flow in a Channel Against An inclined Wall with surface tension Effect,INTERNATIONAL CONFERENCE ON APPLIED ANALYSIS AND ALGEBRA,YIDIZ TECHNICAL UNIVERSITY ISTANBUL, TURKEY