An-Najah Blogs :: Naji Qatanani An-Najah Blogs :: Naji Qatanani en-us Sat, 02 Jul 2022 07:30:28 IDT Sat, 02 Jul 2022 07:30:28 IDT Numerical Methods for Solving Fuzzy Fredholm Integral Equation of the Second Kind ArticlesIn 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 To demonstrate the credibility of these numerical schemes we consider a numerical test examlple The numerical results show to be in a close agreement with the exact solutionComputational Methods for Solving Fredholm Integral Equation of the Second Kind ArticlesThe 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 numerical results of test examples are also included to verify the performance of the proposed algorithmsAsymptotic Error Analysis for the Heat Radiation Boundary Integral Equation ArticlesIn 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 available theoretical resultsdThe Mathematical Structure and Analysis of an MHD Flow in Porous Media ArticlesThis 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 are employed for the flow through the poprous media The solutions obtained for the Riabouchinsky-type flows are then classified into different typesMagnetohydrodynamic Rayleigh Problem with Hall Effect ArticlesThis paper gives very significant and up-to-date analytical and numerical results to the MHD 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 Numerical values for the effects of the Hall parameter N and the Hartmann number M on the velocity components u and v are tabulated and their profiles are shown graphically The numerical results show that the velocity component u increases with the increase of N and decreases with the increase of M Whereas the velocity component v increases with the increase of both M and N These numerical results have shown to be in a good agreement with the analytical solutionNumerical Treatment of Strongly Elliptic Integral Equation ArticlesThe 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 integral equation The concept of the principle symbol allows the characterization of the boundary integral equation whose vartiational formulation on the boundary provides there a Garding inequality Therefore the Galerkin method can be analyzed similarly to the domain finite element methods providing asymptotic convergence if the number of grid points increases These asymptotic error analysis will be presented in details To illustrate the efficiency of the Galerkin boundary element method we consider as an numerical experiment the strongly elliptic boundary integral equation with the logarithmic single layer potential Consequently we use the Gaussian elimination method as a direct solver and the conjugate gradient iteration to solve the positive definite linear system A comparison is drawn between these methodsOn Existence and Uniqueness Theorem Concerning Time-Dependent Heat Transfer Model ArticlesIn 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 the uniqueness of a weak solution for this problem The existence of the solution can be proved by solving an auxiliary problem by the Galerkin-based approximation method and Moser-type arguments which implies the existence of solution to the original problem The uniqueness of the solution will be proved by using the same approach in our previous work for the stationary heat transfer model and some ideas from nonlinear heat conduction analysisNumerical Simulation of The Steady State Heat Conduction Equation ArticlesThe main concern in this article is the numerical realization 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 descritization of the conduction integral equation we have used the boundary element method based on the Galerkin-Bubnov scheme The system of linear equations has been solved by the conjugate gradient- method with preconditioning To demonstrate the high efficiency of this method a numerical experiment has been constucted for a three- dimensional simple pipe