Bachir Nour KharratEbla Private university andAleppo University facultyof scienceMathematics department
Bachir Nour Kharrat
Ph.D,D.Sc
About
58
Publications
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66
Citations
Citations since 2016
Introduction
Bachir Nour Kharrat currently works at the Department of Mathematics, Aleppo University,and Ebla Private University. Their current project is 'Approximate solutions of boundary value problems'.
Skills and Expertise
Additional affiliations
January 1983  present
Publications
Publications (58)
In this paper, we give an approximate mathematical model of a periodically nonhomogeneous LoveKirchhoff plate with periodic inclusions or perforations, that means a mechanical structure in the linear elasticity theory with periodic structure. Dealing with the variational formulation, we prove the existence and the uniqueness of a weak solution. T...
In this paper, we apply a new modified homotopy perturbation method to find approximated solutions for nonlinear Boundary value problems. A reliable modification of the homotopy perturbation method is proposed, and the modified method is employed to solve some nonlinear Boundary value problems; the results are compared with those obtained by the or...
R.J.of.Aleppo Univ . Science Series Series 2022 No. 157
Modified of Picard Iteration Method Using Chebyshev
Polynomials of the First Type for Solving Sine –Gordan
Problem
Iman Rajab Basha*, Bachir Nour Kharrat**,.Ghada Joujeh***
*Post Graduate student (PhD), Dept of Mathematics, Faculty of science, University
of Aleppo
**Prof, Dept of Mathematics,...
This paper intends to provide the Helaplace method to solve several applications derived from Application Mathematics. These applications have been solved using different approaches as follows:EmdenFlower equation , which is a problem of initial values represented with a differential equation of 2 nd order which represents an astronomy motion ....
In this work, we apply hybrid Variational Iteration Method (VIM) with Mohand integral transform hybrid Adomian Decomposition Method (ADM) with Mohand integral transform and Homotopy Perturbation Method (HPM) with Mohand integral transform to solve some of Weakly Singular IntegroDifferential Equations, and in order to show the accuracy and effectiv...
The aim of this paper is to modify the Homotopy Perturbation method by using the Elzaki transform and representing the nonlinear part by DaftardarGejje and Jafari polynomials .To show effectiveness of the proposed method.We apply it on two applications which represent the Riccati equation and the Damping Duffing equation ,and then comparing the ob...
The aim of this paper is to modify the Homotopy Perturbation method by using the Elzaki transform and representing the nonlinear part by DaftardarGejje and Jafari polynomials .To show effectiveness of the proposed method.We apply it on two applications which represent the Riccati equation and the Damping Duffing equation ,and then comparing the ob...
In the present work, variational iteration method is combined with KharratToma transform method
to solve nonlinear problems. Some illustrative numerical examples are given. The solutions obtained by this
method show the accuracy and the efficiency of the suggested combined method
In this work, we apply two hybrid Adomian Decomposition Method (ADM) with Mohand integral transform and Homotopy Perturbation Method (HPM) with Mohand integral transform to solve some of Delay Volterra IntegroDifferential Equations of Pantograph type arising in engineering and physical applications. We have obtained the exact solutions of these eq...
In this work, we propose a new modification to the method
of Variational Iteration Method (VIM) by hybridizing it with
the Mohand Integral Transformation to solve some Volterra
IntegoDifferential Equations, and in order to show the
accuracy and effectiveness of the proposed method, we have
applied it to several different forms of IntegralDif...
In this paper, we hybrized the Variational Iteration Method (VIM) using ZZ transform (VIZZTM), which is a semianalytic method based on finding the solution of the problem by using correction functional and using ZZ transform. Some applications are given to show the accuracy and effectiveness of the proposed modification.
The aim of this study is to establish duality relations between ZZ transform and some integral transforms namely Laplace transform, Sumudu transform, Natural transform and Aboodh transform. It is very difficult to apply some of the transforms to solve differential and integral equations due to its complexity. However, taking advantage from the dual...
This paper presents a modified genetic programming to find exact or approximate solution of various nonlinear boundary value problems represented by partial differential equations with boundary conditions. Genetic programming is a metaheuristic algorithm that belongs to the evolutionary algorithms, which simulates some of the ideas of natural evolu...
In this paper, we modified Adomian Decomposition Method (ADM) by hybrid it with a new integral transform KharratToma transform (KTADM). To demonstrate the accuracy and effectiveness of the proposed method, it was applied to solve many mathematical models. We got the exact solution in some problems and deliberately compared the accuracy of error in...
In this paper ,We propose a hybrid Variational Iteration Method with Elzaki transform and Padé technique (VIMElzakiPadé) to solve initial and boundary values problems. some applications are given to show the accuracy and by reaching to the exact solution for application No. 3 and the approximate solution in other applications (No. 1, No. 2) that...
The purpose of this paper is to develop the Homotopy Perturbation method by using the Natural transform and representing the nonlinear part by DaftardarGejje and Jafari polynomials .To show effectiveness of the proposed method.We apply it on two applications which represent two different forms for Van Der Pol oscillator,and then comparing the obta...
This article introduces a new hybridization between the KharratToma transform and the homotopy perturbation method for solving a strongly nonlinear oscillator with a cubic and harmonic restoring force equation that arising in the applications of physical sciences. The proposed method is based on applying our new integral transform "KharratToma Tr...
This article introduces a new hybridization between the KharratToma transform and the homotopy perturbation method for solving a strongly nonlinear oscillator with a cubic and harmonic restoring force equation that arising in the applications of physical sciences. The proposed method is based on applying our new integral transform "KharratToma Tr...
In this paper, we propose a new integral transform, called the KharratToma Transform which can be considered as a base for a number of potential new integral transforms. Many fundamental properties about this new integral transform which were created in this work, include (for example) the existence theorem, transportation theorem, convolution the...
In this paper, numerical solution of different order Fuzzy boundary value problems are presented using Least square method. Fuzzy function is proposed which is made to satisfy the fuzzy boundary conditions given,and used to generate the residual to be minimized. To investigate the effectivensee of the method, numerical examples were considered whic...
In this paper, we proposed expanding the application of genetic algorithm for solving some nonlinear singular boundary value problems arising in physiology applications which it is difficult to solve this type of problems because of a singularity at the boundary point x= 0. Genetic Algorithm is one of the evolutionary algorithms that uses principle...
Modification Of Differential Transform Method Using Sumudu Transform And Padé Approximation For Solving Some Nonlinear Initial And Boundary Value Problems
, and
*Post Graduante Student (MSc), Dept of Mathematics, Faculty of Science, University of Aleppo
**Dept of Mathematics, Faculty of Science, University of Aleppo
Abstract
The purpose of our pape...
The aim of this work is to apply the finite element method for modeling the middle ear by using ANSYS 16 program, Then to find 100 mode shape of the vibrations of the middle ear and we also find the stress tensor in the middle ear by applying sound pressure of 90dB on the tympanic membrane. The value of stress may be consider as measure of the safe...
Abstract: This paper introduces an efficient proposed technique combining the homotopy perturbation method
and natural transform to obtain a numerical solution of an important initial value problem arising in applied
dynamics, called Van Der Pol Oscillator problem. The objective of this work is to investigate the efficiency of
this proposed hybrid...
In this paper, we present a new combination between the natural transform and the homotopy perturbation method. This hybrid technique allows to obtain numerical and analytical solutions for initial value problems represented by nonlinear partial differential equations of a various normal orders. This presented method depends on applying the natura...
In this paper, we introduce a numerical treatment using the generalized Euler method (GEM) for the fractional (Caputo sense) Riccati and Logistic differential equations. In the proposed method, we invert the given model as a difference equation. We compare our numerical solutions with the exact solution and with those numerical solutions using the...
This paper introduces an efficient proposed technique combining the homotopy perturbation method and natural transform to obtain a numerical solution of an important initial value problem arising in applied dynamics, called Van Der Pol Oscillator problem. The objective of this work is to investigate the efficiency of this proposed hybrid method. Th...
In this paper, we proposed expanding the application of the He's homotopy perturbation method to solve nonlinear algebraic equations using the first seven terms of Taylor's series. The main objective of our research is to find an approximate solution with high accuracy for solving nonlinear algebraic equations. In the proposed hybrid scheme, we co...
Abstract
The aim of this work is to apply the differential transform method to solve initial and boundary value problem for ordinary differential equation of 15𝑡ℎorder,we applied the method to linear and nonlinear initial and boundary value problem for ordinary differential equation of fifteenth order. To show the accuracy and effectiveness of this...
In this paper, a combination between a sumudu transform (ST) and the homotopy perturbation
method (HPM) is presented. This combination allows to obtain approximate and exact solutions for linear and
nonlinear boundary value problems. The results obtained by the proposed hybrid method (STHPM) reveal that
is very effective and convenient.
In this paper, a combination between a sumudu transform (ST) and the homotopy perturbation method (HPM) is presented. This combination allows to obtain approximate and exact solutions for linear and nonlinear boundary value problems. The results obtained by the proposed hybrid method (STHPM) reveal that is very effective and convenient.
In this paper, we obtain exact and approximate solutions for system of linear and nonlinear ordinary differential equations using differential transform method (DTM). The results show that the DTM lead to accurate results and they indicate that only a few terms lead to accurate solutions.
In this paper, we present a modification to homotopy perturbation method for solving nonlinear
Boundary value problems., Some examples are given, revealing its effectiveness and convenience. Also the
results obtained by modified homopy perturbation method (MHPM) is superior to that obtained by the original
homotopy perturbation method
In this paper, we present a modification to homotopy perturbation method for solving nonlinear
Boundary value problems., Some examples are given, revealing its effectiveness and convenience. Also the
results obtained by modified homopy perturbation method (MHPM) is superior to that obtained by the original
homotopy perturbation method
In this paper, a general framework of the differential transform method (DTM) is presented for solving strongly nonlinear initial value problems represented by ordinary differential equations. This technique doesn't require any discretization, linearization or small perturbation and therefore it reduces significantly the numerical computation. So a...
In this paper, we give an approximate mathematical model of a periodically nonhomogeneous
LoveKirchhoff plate with periodic inclusions or perforations. Dealing with the variational formulation, we prove
the existence and the uniqueness of a weak solution. The asymptotic expansion is used to derive the
homogenized approximate problem and the first...
In this work, semianalytical approximate technique (Homotopy Perturbation Method) was applied to obtain the solution of fluid flow in a porous media. The governing equations with variable pressure in two dimensional cartesian coordinates can be represented by nonlinear Navier Stokes equations. An illustrative application is provided to demonstrate...
In this paper, we present a hybrid method for solving nonlinear heat transfer equations, by using genetic programming (GP) with homotopy perturbation method (HPM). The main advantage of hybrid method is that the obtained solution leads to a small error solution at all points in the solution interval. While the resulting solution obtained byapplying...
In this paper, differential transform method (DTM) is applied to linear and nonlinear initial and boundary value problems represented by ordinary differential equations of 14th order. So as to show the capability and robustness, some examples are solved as numerical examples that we are compared our results with the Homotopy perturbation method (HP...
In this paper, we study the solutions of the linear and nonlinear threedimensional Fredholm integral equations by developing the regularization method which is used for the one and twodimensional equations. Then we apply some of the semianalytic methods (Homotopy perturbation method HHPM, Adomian decomposition method ADM). We also study the exis...
In this paper, we apply the variational iteration method for solving twodimensional and the thirddimensional volterra integral equation of the second kind , and we also assert the a curacy and effectiveness of this method through some application and compare them with numerical methods which use in the two works [ 1,2 ]
In this paper, we apply the variational iteration method for solving twodimensional and the thirddimensional volterra integral equation of the second kind , and we also assert the a curacy and effectiveness of this method through some application and compare them with numerical methods which use in the two works [ 1,2 ]
In this paper, we propose a hybrid Homotopy Perturbation Method with Fourier transform, we show the accuracy and effectiveness of this method by several applications with respect to the difference values of u m diffusion coefficient in the porous media equation.
In this paper, we propose a new approximate solution, namely modified Homotopy Perturbation Sumudu transform method (MHPSTM) to handle various system of nonlinear partial differential equations.
The modified Homotopy Perturbation Sumudu transform method is a combined form of the Homotopy Perturbation method and the Sumudu transform. We test our mod...
In this paper, we propose a new approximate solution, namely modified Homotopy Perturbation Sumudu transform method (MHPSTM) to handle various system of nonlinear partial differential equations.
The modified Homotopy Perturbation Sumudu transform method is a combined form of the HomotopyPerturbation method and the Sumudu transform. We test our modi...
solution, namely modified Homotopy Perturbation Elzaki
transform method (MHPETM) to handle various linear and
nonlinear integrodifferential equations. The modified
Homotopy Perturbation Elzaki transform method is a
combined form of the Homotopy Perturbation method and
the Elzaki transform. We test our modified method on some
example and compare th...
Abstract: In this paper, we propose a new approximate solution, namely modified Homotopy Perturbation
Sumudu transform method (MHPSTM) to handle various system of nonlinear partial differential equations.
The modified Homotopy Perturbation Sumudu transform method is a combined form of the Homotopy
Perturbation method and the Sumudu transform. We te...
In this paper, we study the solutions of the linear and nonlinear threedimensional Fredholm integral equations by developing the regularization method which is used for the one and two–dimensional equations. Then we apply some of the semianalytic methods (Homotopy perturbation method HHPM, Adomian decomposition method ADM). We also study the exis...
1
t
Adomian Decomposition Method is a New technique wish has been using to solvelinear and nonlinear Initial and Boundary value problems. In this work we propose to apply ADM to solvelinear and nonlinear Difference Equations of first and high order.The aim of this paper is to propose a new modified method by using ZAdomian Decomposition Method we...
In this paper we present an improved Homotopy Perturbation Method for the approximated solutions for nonlinear Boundary value problems. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors. Several examples are given to verify the reliability and efficiency of the method.

In this In this paper He's Homotopy Perturbation Method (HHPM) is extended to solve nonlinear Algebraic equations by using the first six terms of a
Taylor's series in Newton method.
Several test problems are given to show the efficiency
and the accuracy of proposed iterative scheme
The traditional perturbation methods depend on a “small parameter” which is difficult to be determined for some realapplications .To overcome address this shortcoming, A new powerful semianalytical method the Adomian decomposition method (ADM) is introduced to approximate the deflection of polysilicon diaphragm with small flexural rigidity of Mic...
In this paper, we give an approximate mathematical model of a periodically nonhomogeneous LoveKirchhoff plate with periodic inclusions or perforations, that means a mechanical structure in the linear elasticity theory with periodic structure.
Dealing with the variational formulation, we prove the existence and the uniqueness of a weak solution. T...
Abstract
The traditional perturbation methods depend on a “small parameter” which is difficult to be determined for some realapplications .To overcome address this shortcoming, A new powerful semianalytical method the Adomian decomposition method (ADM) is introduced to approximate the deflection of polysilicon diaphragm with small flexural rigid...
In this work we have studied the problem of motion of a heavy magnetized gyrostat carrying electric charges and acted upon by uniform electric and magnetic fields in addition to gravity. The equilibrium positions of the gyrostat have been found and their stability studied.
Résumé de la thèse؛
Dans cette thèse, nous donnons un modèle mathématique approché d'une plaque de LoveKirshoff périodiquement non homogène avec des inclusions ou des perforations périodiques, c'estàdire une structure mécanique dans la théorie de l'élasticité linéaire avec une structure périodique. A partir de la formulation variationnelle, nous...
The aim of this paper is to study the
homogenization of some non self adjiont eigenvalues
problems corresponding to elliptic differential operators.
Questions
Questions (11)
The basic elasticity equations can be written in terms of the six stress components ,the methods to solve these equations are few,so I am looking for effective ways to solve these equations.
Many Boundary Value problems can be solved by numerical methods ,l,am looking for the possibilty of combining some numerical methods with some integral transforms in order to speed the convergence
Fuzzy boundary broblems have many applications ,so it's very important to compined seminumericale methods as HPM,VIM,and ADM,......with some artificial algorithms.
Many semeanalytical method as HPM,HVIM,ADM,..etc have been modified using some integral transformes,so I'm looking for researches related with the above question.
Fuzzy differential equations have many applications therefore,it is necessary to make sure that is at least one solution or more than one to this equation before looking for any method to solve it.
Fuzzy boundary value problems have many applications ,so the issue of the existence and the uniqueness of the solutions is very important .
TheأHomotopy perturbation method depends on finding the solution in an iterative manner, and this is related to the speed of convergence. Therefore, it is necessary to link the speed of convergence with two parameters.
Composite materials have many applications, especially in the case of heterogeneous materials of periodique composition
there are many theoritical papers about FBVP you and FIP ,so there is need for some practical applications
Projects
Projects (7)
“Studying and Developing Approximate Solutions for Integro Differential Equations Problems and Some of their Applications”