M. MERZOUGUI Abdelkrim

Prof

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 : abdelkrim.merzougui@univ-msila.dz

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Recent Publications

2024-07-23

Two dimensional free surface flows over submerged obstacles

In this work, we study the problem of steady two-dimensional flows over multiple obstacles under the effects of gravity and surface tension in fluid of a constant depth, and in the presence of a uniform stream. The fluid is treated as inviscid and incompressible. The flow is assumed to be irrotational. The problem is solved numerically by using the boundary integral equation technique, based on Cauchy integral formula. It is shown that, for both supercritical and subcritical flows, solutions depend on three parameters: the Froude number F, the Weber number δ and the angles of obstacles γ and β. Finally, solution diagrams for all flow regimes are presented.
Citation

M. MERZOUGUI Abdelkrim, Abdelkader Laiadi, , (2024-07-23), "Two dimensional free surface flows over submerged obstacles", [national] Sohag J. Math. , naturalspublishing

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2023

Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative

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

M. MERZOUGUI Abdelkrim, (2023), "Finite Difference Approximation for the Space-Time Fractional Linear Diffusion Equation Involving the Caputo-Hadamard Fractional Derivative", [national] International Journal of Applied and Computational Mathematics , Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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2022

The numerical solution of the space-time fractional diffusion equation involving the Caputo-Katugampola fractional derivative

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

M. MERZOUGUI Abdelkrim, (2022), "The numerical solution of the space-time fractional diffusion equation involving the Caputo-Katugampola fractional derivative", [national] Numerical Algebra, Control and Optimization , Bulent Karasozen

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Numerical solutions for linear fractional differential equation with dependence on the Caputo-Hadamard derivative using finite difference method

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

M. MERZOUGUI Abdelkrim, (2022), "Numerical solutions for linear fractional differential equation with dependence on the Caputo-Hadamard derivative using finite difference method", [national] Palestine Journal of Mathematics , Nouressadat Touafek

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2019-12-22

تدفق سائل ذي سطح حرّ فوق عقبات شبه منحرفة مع تأثير الجاذبيّة والتّوتّر السّطحيّ

في هذا العمل، ندرس التّدفّقات ثنائيّة الأبعاد على عقبات شبه منحرفة تحت تأثير الجاذبيّة والتّوتّر السّطحيّ في المياه ذات العمق الثّابت. نفترض أنّ السّائل غير قابل للضّغط وليس لزجا. نفترض أنّ التّدفّق ليس دورانيّا. يتمّ حلّ المسألة عدديًّا باستخدام تقنيّة المعادلة التّكامليّة الحدوديّة، استنادًا إلى صيغة تكامل كوشي. يتبيّن انّه بالنّسبة لكلّ من التّدفّقات فوق الحرجة وتحت الحرجة، تعتمد حلول هذه المسألة على ثلاثة معاملات: (1) عدد فرود 3) زوايا العقبات. توجد عائلات متعدّدة من الحلول لقيم معيّنة للمعاملات Weber2) عدد ويبر Froude الثّلاثة السّابقة، سوف نناقش هذه النّتائج في نهايّة هذه الورقة.
Citation

M. MERZOUGUI Abdelkrim, Abdelkader Laiadi, , (2019-12-22), "تدفق سائل ذي سطح حرّ فوق عقبات شبه منحرفة مع تأثير الجاذبيّة والتّوتّر السّطحيّ", [national] مجلة العلوم والتكنولوجيا , مجلة العلوم والتكنولوجيا

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2019-11-21

Fractional Differential Equations of Caputo- Katugampola Type and numerical Solutions

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

M. MERZOUGUI Abdelkrim, (2019-11-21), "Fractional Differential Equations of Caputo- Katugampola Type and numerical Solutions", [international] RAMA 11 , Sidi Bel Abbès

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2019

Free surface flows over a successive obstacles with surface tension and gravity effects

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

M. MERZOUGUI Abdelkrim, Abdelkader Laiadi, , (2019), "Free surface flows over a successive obstacles with surface tension and gravity effects", [national] AIMS Mathematics Journal , AIMS Press

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2018

NUMERICAL SOLUTION FOR A FREE SURFACE FLOW OVER MULTIPLE OBSTACLES

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

M. MERZOUGUI Abdelkrim, ABDELKADER LAIAD, , (2018), "NUMERICAL SOLUTION FOR A FREE SURFACE FLOW OVER MULTIPLE OBSTACLES", [national] Electronic Journal of Mathematical Analysis and Applications (EJMAA) , EJMAA

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2017

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

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

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

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EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR A THIRD-ORDER DELAY DIFFERENTIAL EQUATION

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

M. MERZOUGUI Abdelkrim, FARID NOUIOUA, ABDELOUAHEB ARDJOUNI, , (2017), "EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR A THIRD-ORDER DELAY DIFFERENTIAL EQUATION", [national] International Journal of Analysis and Applications , IJAA

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2016

Approximate solution for linear Fredholm integral equation by using Bernstein polynomials

Approximate solution for linear Fredholm integral equation by using Bernstein polynomials
Citation

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

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

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

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

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

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

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

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Non Linear Free-Surface Flow Over a Submerged Obstacle

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

M. MERZOUGUI Abdelkrim, Abdelkader. Laiadi, , (2016), "Non Linear Free-Surface Flow Over a Submerged Obstacle", [national] General Letters in Mathematics(GLM) , REFAAD

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2015

Numerical of free surface flow under gate

Numerical of free surface flow under gate
Citation

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

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2014

Free-Surface Flow over Triangular Obstacle

Free-Surface Flow over Triangular Obstacle
Citation

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

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Numerical solution for free surface flow over multiple Obstacles

Numerical solution for free surface flow over multiple Obstacles
Citation

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

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FREE SURFACE FLOW OVER A TRIANGULAR DEPRESSION

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

M. MERZOUGUI Abdelkrim, Abdelkader Laiadi, , (2014), "FREE SURFACE FLOW OVER A TRIANGULAR DEPRESSION", [national] TWMS J. App. Eng. Math. , FEYZİYE SCHOOLS FOUNDATION IŞIK UNIVERSITY Faculty of Arts and Sciences

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2012

Free-Surface Flow over a step

Free-Surface Flow over a step
Citation

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

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2011

A waveless Two-Dimentional flow in a Channel Against An inclined Wall with surface tension Effect

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

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

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