Naji Qatanani

Naji Qatanani
An-Najah National University · Department of Mathematics

Ph.D

About

60
Publications
5,224
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224
Citations
Introduction

Publications

Publications (60)
Article
Full-text available
The present study investigates the effect of mathematical modeling on conceptual understanding among student-teachers. Also, the study proposes relevant materials and activities in mathematical modeling. Two classes of 140 student-teachers participated in the study. Mathematical modeling instruction was used in the treatment group, while the compar...
Article
Full-text available
In this paper, we propose two numerical methods, namely: Gauss-Jacobi and Gauss-Seidel iterative schemes to solve the Positive Triangular Fully Fuzzy Linear System. A description of these numerical schemes and their convergence properties have been presented. Numerical example with known exact solution are given to illustrate the efficiency of the...
Article
Science, technology, engineering and mathematics (STEM) is a comprehensive approach that integrates those disciplines into a cohesive learning paradigm. Applying this approach is very important to modernize teaching strategies in order to provide the current competitive and skill-based job market. This study aims to investigate the impact of using...
Article
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In this paper, a collocation method using sinc functions and Chebyshev wavelet method is implemented to solve linear systems of Volterra integro-differential equations. To test the validity of these methods, two numerical examples with known exact solution are presented. Numerical results indicate that the convergence and accuracy of these methods...
Preprint
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In this article, two numerical techniques, namely, the homotopy perturbation and the matrix approach methods have been proposed and implemented to obtain an approximate solution of the linear fractional differential equation. To test the effectiveness of these methods, two numerical examples with known exact solution are illustrated. Numerical expe...
Article
Full-text available
Two numerical techniques, namely, Haar Wavelet and the product integration methods, have been employed to give an approximate solution of the fractional Volterra integral equation of the second kind. To test the applicability and efficiency of the numerical method, two illustrative examples with known exact solution are presented. Numerical results...
Article
In this article we study balanced model reduction of linear control systems using the singular perturbation approximation. Balanced model reduction techniques have been successfully applied to systems with homogeneous initial conditions, with one of their most important features being a priori L 2 and H ∞ bounds for the approximation error. The mai...
Article
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In this article we focus on the balanced truncation linear quadratic regulator (LQR) with constrained states and inputs. For closed-loop, we want to use the LQR to find an optimal control that minimizes the objective function which called "the quadratic cost function" with respect to the constraints on the states and the control input. In order to...
Article
In this article we study balanced model reduction of linear systems for feedback control problems. Specifically, we focus on linear quadratic regulators with collocated inputs and outputs, and we consider perturbative approximations of the dynamics in the case that the Hankel singular values corresponding to the hardly controllable and observable s...
Article
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Three numerical schemes, namely: Toeplitz Matrix meth-od, Product Nystrom method and Sinc-Collocation method have been proposed and implemented to give an approximate solution of the linear Volterra integral equation of the second kind with Carleman kernel. To display the validity and acceptability of the numerical methods, two illustrative example...
Article
Full-text available
In this article, we present up to date results on the balanced model reduction techniques for linear control systems, in particular the singular perturbation approximation. One of the most important features of this method is it allows for an a priori L 2 and H ∞ bounds for the approximation error. This method has been successfully applied for syst...
Article
Full-text available
In this article, three numerical iterative schemes, namely: Jacobi, Gauss–Seidel and Successive over-relaxation (SOR) have been proposed to solve a fuzzy system of linear equations (FSLEs). The convergence properties of these iterative schemes have been discussed. To display the validity of these iterative schemes, an illustrative example with know...
Article
Full-text available
Finite element solution of unsteady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible viscous fluid past through porous medium between two parallel plates is presented in the presence of a transverse magnetic field and Hall effect. The results obtained from some test cases are then compared with previous published work u...
Article
Full-text available
Two numerical schemes, namely, the Taylor expansion and the variational iteration methods, have been implemented to give an approximate solution of the fuzzy linear Volterra integral equation of the second kind. To display the validity and applicability of the numerical methods, one illustrative example with known exact solution is presented. Numer...
Article
Full-text available
In this article some numerical methods, namely: the Taylor expansion method and the Trapezoidal method have been implemented to solve a fuzzy Fredholm integral equation of the second kind. Consequently, we convert a linear fuzzy Fredholm integral equation of the second kind into a linear system of integral equations of the second kind in crisp case...
Article
In this article we present some analytical and numerical methods for solving magnetohydrodynamic (MHD) flow past an impulsively started infinite horizontal flat plate in a rotating system. An exact solution based on Laplace transform has been presented. This method has shown to be very efficient in solving these types of problems. For the numerical...
Article
The main purpose of this paper is the numerical solution of the one-dimensional linear Fredholm integral equation of the second kind by the collocation and the Nystroem methods using the Lagrange basis functions for piecewise linear interpolation. Some effective algorithms implementing these methods using Matlab software have been constructed. The...
Article
Full-text available
We consider the integral equation arising as a result of heat radiation exchange in both convex and nonconvex enclosures of diffuse grey surfaces. For nonconvex geometries, the visibility function must be taken into consideration. Therefore, a geometrical algorithm has been developed to provide an efficient detection of the shadow zones. For the nu...
Article
This article focuses on developing and examining several numerical algorithms used to construct higher order Taylor methods for approximating the solution of a system of first order initial value problems. Some numerical test cases to demonstrate the efficiency of these algorithms are presented. The numerical results have shown to be consistent wit...
Article
Full-text available
In this paper a rigorous convergence and error analysis of the Galerkin boundary element method for the heat radiation integral equation in convex and non-convex enclosure geometries is presented. The convergence of the approximation is shown and quasi-optimal error estimates are presented. Numerical results have shown to be consistent with availab...
Article
This article is concerned with the formulation and analytical solution of equations for modeling a steady two-dimensional MHD flow of an electrically conducting viscous incompressible fluid in porous media in the presence of a transverse magnetic field. The governing equations, namely, Navier-Stokes equations and the Darcy-Lapwood-Brinkman model ar...
Article
This paper gives very significant and up-to-date analytical and numerical results to the magnetohydrodynamic flow version of the classical Rayleigh problem including Hall effect. An exact solution of the MHD flow of incompressible, electrically conducting, viscous fluid past a uniformly accelerated and insulated infinite plate has been presented. N...
Article
An attempt is made to study the steady MHD plane aligned flow through porous media in the presence of a magnetic field. An alternative approach to the Riabouchinsky method is developed for this flow problem. The proposed method will reduce the number of arbitrary constants arising when using the Riabouchinsky method. Consequently, many of the restr...
Article
Full-text available
The main concern in this article is the numerical realisation of the steady state heat conduction taking place in a three-dimensional enclosure geometries. For that purpose we have derived the integral equation of heat conduction from the original boundary value problem using the weighted residual method. For the discretisation of the conduction in...
Article
Full-text available
This paper is concerned with the numerical handling of the governing equations for the radiative heat transfer in a gray, emitting, absorbing and scattering medium which is bounded by gray, diffuse, emitting and reflecting surfaces. For the numerical realization of the coupled governing equations we use the well-known boundary element method based...
Article
In this article we consider a physical model describing time-dependent heat transfer by conduction and radiation. This model contains two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-grey surfaces. The aim of this work is to present a reliable framework to prove the existence and...
Article
This paper presents an efficient computational exhaustive method that permits to calculate both upper and lower response-time bounds for CAN messages. Response-time analysis for CAN messages is relatively limited for computations of the worst case situation. It is computed assuming a maximum transmission time and critical instant releasing of messa...
Article
Full-text available
The boundary integral equation of heat radiation for non-convex enclosure geometries is discretized using the boundary element collocation method. This yields the linear system (I −Kn)qn = gn. This linear system is solved using the multigrid iterative method. Then a fast solver method is used to solve the linear system Aq = g where A = (I − K). The...
Article
Full-text available
This paper presents an efficient computational exhaustive method that permits to calculate both upper and lower response-time bounds for CAN messages. Response-time analysis for CAN messages is relatively limited for computations of the worst case situation. It is computed assuming a maximum transmission time and critical instant releasing of messa...
Article
Full-text available
This paper is concerned with the numerical handling of the governing equations for the radiative heat transfer in a gray, emitting, absorbing and scattering medium which is bounded by gray, diffuse, emitting and reflecting surfaces. For the numerical realization of the coupled governing equations we use the well-known boundary element method based...
Article
This paper presents an efficient computational exhaustive method that permits to calculate both upper and lower response-time bounds for CAN messages. Response-time analysis for CAN messages is relatively limited for computations of the worst case situation. It is computed assuming a maximum transmission time and critical instant releasing of messa...
Article
Full-text available
Explicit flow of the radiative energy between two points in a three-dimensional convex enclosure with diffuse and gray surface leads to a Fredholm integral equation of the second kind. Some existing results on the behavior of this equation for smooth and piecewise surfaces are presented. A boundary element method based on the collocation discretiza...
Article
Full-text available
This article gives very significant and up-to-date analytical results on the conductive-radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-gray surfaces. Some properties of the radiative integral operator will be presented. The main emphasis...
Article
We study in this paper and analyse a model for the radiative heat transfer in bodies that are conductive, grey and semitransparent. One of the most important properties of this model is the non-local interaction due to the radiation exchange. This, together with the nonlinearity arising from the well-known Stefan-Boltzmann law, makes the resulting...
Article
Full-text available
The integral equation describing the flow of the radiative energy between two points on a three-dimensional surface is derived. The boundary element method is used for the discretization of the integral equation of heat radiation by a locally based interpolation function and nodal collocation. We describe an efficient algorithm for the computation...
Article
Full-text available
Explicit flow of the radiative energy between two points in a three-dimensional convex enclosure with diffuse and gray surface leads to a Fredholm integral equation of the second kind. Some existing results on the behavior of this equation for smooth and piecewise surfaces are presented. A boundary element method based on the collocation discretiza...
Article
In this article we consider heat transfer in a non-convex system that consists of a union of finitely many opaque, conductive and bounded objects which have diffuse and grey surfaces and are surrounded by a perfectly transparent and non-conducting medium (such as vacuum). The resulting problem is non-linear and in general is non-coercive due to the...
Article
This article deals with the mathematical and the numerical aspects of the Fredholm integral equation of the second kind arising as a result of the heat energy exchange inside a convex and non-convex enclosure geometries. Some mathematical results concerning the integral operator are presented. The Banach fixed point theorem is used to guarantee the...
Article
Full-text available
In this article we present a very effective numerical solution for the three-dimensional heat radiation boundary integral equation. Some approximation methods for the full dense matrices are reviewed. The adaptive cross approximation (ACA) has been introduced and then used for the compression of the boundary element system matrix.Some numerical exp...
Article
Full-text available
In this article we present a very effective numerical solution for the three-dimensional heat radiation boundary integral equation. Some approximation methods for the full dense matrices are reviewed. The adaptive cross approximation (ACA) has been introduced and then used for the compression of the boundary element system matrix. Some numerical ex...
Article
Full-text available
The radiation exchange in both convex and non-convex enclosures of diffuse gray surfaces is given in the form of a Fredholm boundary integral equation of the second kind. A boundary element method which is based on the Galerkin discretization schem is implemented for this integral equation. Four iterative methods are used to solve the linear system...
Article
In this article we focus our attention on the finite element error analysis for a problem involving both conductive and radiative heat transfer. We sketch the main steps of the analysis by stating the required a priori estimates and the final estimates. The proof for the estimate of the error due to approximation of the geometry is also presented....
Article
In this present paper we represent some important mathematical results on the physical model describing the heat transfer by conduction and radiation. The problem to be considered is the heat radiation exchange inside a non-convex body _ containing two conducting and opaque enclosures which are bounded by diffuse and grey surfaces and are surrounde...
Article
Our main concern in this paper is the numerical simulation of the heat radiation exchange in a three-dimensional non-convex enclosure geometry with a diffuse and grey surface. This physical phenomena is governed by a boundary integral equation of the second kind. Due to the non-convexity of the enclosure the presence of the shadow zones must be tak...
Article
Full-text available
This paper gives very significant and up-to-date analytical and numerical results to the three-dimensional heat radiation problem governed by a boundary integral equation. There are two types of enclosure geometries to be considered: convex and nonconvex geometries. The properties of the integral operator of the radiosity equation have been thoroug...
Article
Full-text available
In this article, we develop a set of partial differential equations describing the flow of a dusty fluid in variable porosity media. The developed equations take into account the effect of the porous microstructure on the flowing phases.We presented and overview of the equations governing the flow of a dusty gas in various type media, including tha...
Article
Full-text available
The polar wind is an ambipolar plasma outflow from the terrestrial ionosphere at high latitudes. As the ions drift upward along geomagnetic flux tubes, they move from collision-dominated to collisionless regions. A Monte Carlo simulation was used to calculate the temperature and Coulomb collision frequency in the polar wind. The simulation properly...
Article
The energization of charged particles, due to interaction with electromagnetic turbulence, has an important influence on the plasma outflow in space. The effect of wave-particle interaction (WPI) on O+ and H+ velocity distributions in the polar wind was investigated by using Monte Carlo method. The Monte Carlo simulation included the effect of WPI,...
Article
Full-text available
Altitude profiles for O+ ion velocity distribution functions, O+ parallel and perpendicular temperatures, O+ temperature anisotropy, O+–O+ and O+–O collision frequencies and O+ temperature partition coefficients β|| and β⊥ are obtained in the auroral ionosphere (150 km–500 km). A Monte Carlo simulation was used to investigate the behavior of O+ ion...
Article
Full-text available
The Monte Carlo method was shown to be a very powerful technique in solving the Boltzmann equation by particle simulation. Its simple concept, straightforward algorithm, and its adaptability to include new features (such as, gravity, electric field, geomagnetic field, and different collision models) make it useful tool in space plasma physics, and...
Article
A Maxwell molecule interactions model by the Monte Carlo method is proposed for space plasma simulations. The model describes a collision between a minor ion with a background neutral. As a result of a Maxwell molecule collisions, the magnitude of the relative velocity is unchanged but its direction is altered. However, the velocity of the center o...
Article
For some problems, we obtain analytical solutions to the two-dimensional viscous fluid flows through porous media in the presence of magnetic field. The governing equations are based on Darcy-Lapwood-Brinkman model, and the medium is assumed to be aligned by a magnetic field. Solutions are obtained for Riabouchinsky-type flows, however with a modif...
Article
The energization of charged particles, due to interaction with electromagnetic turbulence, has an important influence on the plasma outflow in space. The effect of wave-particle interaction (WPI) on O+ and H+ velocity distributions in the polar wind was investigated by using Monte Carlo method. The Monte Carlo simulation included the effect of WPI,...
Article
The numerical treatment of boundary integral equations in the form of boundary element methods has became very popular and powerful tool for engineering computations of boundary value problems, in addition to finite difference and finite element methods. Here, we present some of the most important analytical and numerical aspects of the boundary in...

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