One day conference of Numerical Analysis and Optimization
Faculty os Science, Alexandria University
July 26, 2016, Egypt
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  • المؤتمر على روح المغفور لهما الدكتور محمد رفعت عبد السلام والدكتور جمال عبد اللطيف - جامعة سوهاج
  • The Deadlines For Registration has been Postponed Till 15 Jan 2016

List of Abstracts

 
   
 
Title:A multi-domain decomposition based Fourier finite element method for the simulation of 3D marine CSEM measurements
Author Information
Name:Shaaban A. Bakr
University/Institute:Basque Center for Applied Mathematics (BCAM), Mazarredo 14, E48009 Bilbao, Spain. Department of Mathematics, Assiut University, Assiut 71516, Egypt.
Email:shaaban.bakr1@gmail.com
First Additional Author Information
Name:David Pardo
University/Institute:University of the Basque Country (UPV/ EHU), Bilbao, Spain. Basque Center for Applied Mathematics (BCAM), Bilbao, Spain. Ikerbasque, Bilbao, Spain.
Email:
Abstract: We introduce a multi-domain decomposition Fourier finite element (MDDFFE) method for the simulation of three-dimensional (3D) marine controlled source electromagnetic (CSEM) measurements. The method combines a 2D finite element (FE) method in two spatial dimensions with a hybrid discretization based on a Fourier FE method along the third dimension. The method employs a secondary field formulation rather than the full field formulation. By using the secondary field formulation, we avoid to numerically model the source singularities and reduce the effect of the air layer. We apply the MDDFFE method to several synthetic marine CSEM examples exhibiting bathymetry and/or multiple 3D subdomains. Numerical results show that the use of the MDDFFE method reduces the problem size by as much as $87\%$ in terms of the number of unknowns, without any sacrifice in accuracy.
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Title:On the use of rational Chebyshev functions for solving higher-order linear ordinary differential equations with variable coefficients on a semi-infinite domain using two proposed schemes
Author Information
Name:Mahmoud A. Nassar
University/Institute:Mathematics Department, Faculty of Science, Al-Azhar University
Email:m7moudscience@yahoo.com
First Additional Author Information
Name:Mohamed A. Ramadan
University/Institute:Menoufia University
Email:mramadan@eun.eg
Second Additional Author Information
Name:Kamal Raslan Mohamed Raslan
University/Institute:Mathematics Department, Faculty of Science, Al-Azhar University
Email:Kamal_raslan@yahoo.com
Third Additional Author Information
Name:Mahmoud A. Nassar
University/Institute:Mathematics Department, Faculty of Science, Al-Azhar University
Email:m7moudscience@yahoo.com
Abstract: The purpose of this paper is to investigate the use of rational Chebyshev (RC) functions for solving higher-order linear ordinary differential equations with variable coefficients on a semi-infinite domain using two schemes of rational Chebyshev collocation points. This method transforms the higher-order linear ordinary differential equations and the given conditions to matrix equations with unknown rational Chebyshev coefficients. These matrices together with the collocation method are utilized to reduce the solution of higher-order ordinary differential equations to the solution of a system of algebraic equations. The solution is obtained in terms of RC series. Numerical examples are given to demonstrate the validity and applicability of the method. The obtained numerical results are compared with others existing methods and the exact solution where it shown to be very attractive and maintains better accuracy.
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Title:Numerical solutions of second order matrix differential equations using basis splines
Author Information
Name:M. A. Shaalan
University/Institute:Higher Technological Institute, Tenth of Ramadan City, Egypt
Email:abozeid87@yahoo.com
First Additional Author Information
Name:M. A. Ramadan
University/Institute:Faculty of science, Menouifa University, Shebeen El-Koom, Egypt
Email:ramadanmohamed13@yahoo.com
Second Additional Author Information
Name:K. R. Raslan
University/Institute:Faculty of science, Al-Azhar University, Cairo, Egypt
Email:kamal_raslan@yahoo.com
Abstract: This paper is discussed matrix differential equations of second – order with boundary conditions by splines as cubic, quantic and septic splines. Comparisons are shown and advantages of approximation in cubic B-splines method versus cubic splines method with constant term.
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Title:Growth of Vapour Bubble Between two-Phase Density Flow inside a Symmetric Vertical Cylindrical Tube
Author Information
Name:A. K. Abu-Nab
University/Institute:Mathematics Department-Faculty of Science -Menoufia University
Email:ahmed.abunab@yahoo.com
First Additional Author Information
Name:A. K. Abu-Nab
University/Institute:Mathematics Department-Faculty of Science -Menoufia University
Email:ahmed.abunab@yahoo.com
Second Additional Author Information
Name:S. A. Mohammadein
University/Institute:Mathematics Department-Faculty of Science -Tanta University
Email:selimali40_43@yahoo.com
Abstract: The incompressible Newtonian fluid flow with heat transfer in a vertical cylindrical tube is introduced under the assumptions of long wavelength and low Reynolds number. The system of mass, momentum, and energy equations are solved analytically. The mixture flow velocity, bubble growth, and temperature field are obtained for two-phase densities. The growth of vapour bubble and its velocity between two-phase densities are obtained for first time under the effect of Grashof number and constant heating source. The obtained results are compared with Mohammadein et al. model with good agreement.
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Title:Computation Method for Solving MKdV Equation by Galerkin Method with Cubic B-spline
Author Information
Name:zain
University/Institute:Al-Azhar
Email:zainfathi@hotmail.com
First Additional Author Information
Name:Kamal Raslan
University/Institute:Al-Azhar
Email:kamal_raslan@yahoo.com
Abstract: A finite element solution of the modified Korteweg-de Vries (MKdV) equation is set up. It is based on Galerkin’s method using cubic splines as element shape functions. A linear stability analysis shows the scheme is unconditionally stable. Numerical tests for one, two, and three solutions are used to assess the performance of the proposed scheme. The four invariants of motion are evaluated to determine the conservation properties of the algorithm.
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Title:Solving MKdV Equation by Galerkin Method with Cubic B-spline
Author Information
Name:zain
University/Institute:Al-Azhar
Email:zainfathi@hotmail.com
First Additional Author Information
Name:Kamal Raslan
University/Institute:Al-Azhar
Email:kamal_raslan@yahoo.com
Abstract: A finite element solution of the modified Korteweg-de Vries (MKdV) equation is set up. It is based on Galerkin’s method using cubic splines as element shape functions. A linear stability analysis shows the scheme is unconditionally stable. Numerical tests for one, two, and three solutions are used to assess the performance of the proposed scheme. The four invariants of motion are evaluated to determine the conservation properties of the algorithm.
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Title: Cubic B-Spline Method of the Dissipative Wave Equation
Author Information
Name:Dr. Adel R. Hadhoud
University/Institute:M.Sc. , Ph.D. ,Department of Mathematics, Faculty of Science, Menoufia University, Shebeen El-Koom
Email:adelhadhoud_2005@yahoo.com
Abstract: In this paper, a numerical treatment of the nonlinear dissipative wave equation is proposed using collocation method with cubic B-spline over finite elements. For the numerical procedure, time derivative is discretized in the usual finite difference scheme. Solution and its principle derivatives over the subinterval are approximated by the combination of the cubic B-spline and unknown element parameters. Applying the Von-Neumann stability analysis technique we show that the method is conditionally stable. By conducting a comparison between the numerical results and the analytic solution of the equation we will test the accuracy of the proposed method.
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Title:Shallow water model of a thin liquid film on the outer surface of a rotating cylinder
Author Information
Name:Dr. Adel Mohamed Morad
University/Institute:Menoufia University
Email:dr_adel_morad@yahoo.com
Abstract: The shallow water equations describing the motion of a fluid layer on the surface of a rotating cylinder are obtained. It is shown that the equations are similar to the modified Boussinesq equations for shallow water. In other case these equations are similar to the Korteweg–de Vries (KdV) equation whose coefficients take into account the fact that the free boundary of the liquid layer is not a flat surface. For the derivation of the equations the method of multiscale asymptotic expansions and method of the amplitude equations are used.
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Title:Some Generalization of Certain Nonlinear Retarded Integral Inequalities and Their Application
Author Information
Name:Reda Gamal Ahmed
University/Institute:Al-Azhar University
Email:Redagamal@azhar.edu.eg
First Additional Author Information
Name:A. Abdeldaim
University/Institute:Port Said, Suez Canal University
Email:ahassen@su.edu.sa
Second Additional Author Information
Name:A. A. El-Deeb
University/Institute:Al-Azhar University
Email:ahmedeldeeb@azhar.edu.eg
Abstract: The main aim of this disquisition is to investigate some new explicit bounds on solutions to a class of new nonlinear retarded integral inequalities of Gronwall type. We generalize the results presented by Pachpatte in [1] and S. D. Kendre in [2] to nonlinear retarded integral inequalities. With an application to illustrate the interest of our results in the solution of delay nonlinear differential equations with given initial stipulation.
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Title:An interior-point method to solve multi-objective nonlinear programming problem
Author Information
Name:Bothina El-Sobky
University/Institute:Alex
Email:bothinaelsobky@yahoo.com
First Additional Author Information
Name:Y. Aboelnaga
University/Institute:
Email:yousrianaga@yahoo.com
Abstract: An interior-point method to solve multi-objective nonlinear programming problem is introduced. An ε−constraint method is used in this work to convert the multi-objective nonlinear programming problem to single-objective nonlinear programming problem. An active set strategy is used to transform the single-objective nonlinear programming problem to an equality constrained optimization problem. By using a Coleman-Li strategy the iterates which is generated by the proposed algorithm for solving the equality constrained optimization problem are strictly feasible. A preliminary numerical results are reported.
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Title:Ramadan Group(RG) Transform Coupled with Projected Differential Transform for Solving Nonlinear Partial Differential Equations
Author Information
Name:Mohamed Abdel-Latif Ramadan
University/Institute:Department of Mathematics, Faculty of Science, Menoufia University, Shebeen El- Koom
Email:mramadan@eun.eg
Abstract: The main purpose of this short talk is first to introduce the definition of some known integral transforms, namely, Laplace transform, Sumudu transform and Ramadan Group (RG) transform. Then, some structure properties of these transforms will be explored. Secondly, the definition and properties of differential and projected differential transforms will be presented. Finally, a combination of these integral and differential transforms will introduced to solve , analytically, differential equations where will see that a hybrid of RG transform and projected differential transform method is considered to be more efficient and simple to tackle the nonlinear terms in partial differential equations.
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Title:Analytical solution of a boundary-value problem in the frame of second gradient elastic deformation for anisotropic materials in a rectangular domain
Author Information
Name:A. R. El Dhaba
University/Institute:Damanhour University, Faculty of Science.
Email:amrramadaneg@yahoo.com
Abstract: Abstract: Abstract:- A semi-inverse method is used to find analytical solutions for a plane boundary-value problem of linear anisotropic elastic material, in the frame of the second gradient deformation and for a rectangular domain. The solution for the displacement components are expressed as finite sums of elementary functions, with coefficients determined from the boundary conditions, that are imposed in integral form. Two examples are presented for a rectangle subjected to either normal and shear deformation. According to the method that is exploited, the boundary conditions are imposed in integral form.
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Title:Finite difference methods for the nonlinear partial differential equations
Author Information
Name:Kamal R. Mohamed Raslan
University/Institute:Al-Azhar University, Nasr-City, Egypt
Email:Kamal_raslan@yahoo.com
Abstract: The method of finite difference is one of the widely used techniques (together with finite elements and spectral methods …) employed in obtaining numerical solutions of linear and nonlinear ordinary and partial differential equations. Finite difference methods are developed for several physically nonlinear partial differential equations, especially wave equations such as the MEW equation, GRLW and the Hirota equation which is our purpose here. In this talk, I will shed light on the main different techniques of finite difference method to tackle the nonlinear terms of partial differential equations.
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Title:On the optimal control for fractional multi-strain TB model
Author Information
Name:N. H. Sweilam
University/Institute:Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Email:nsweilam@sci.cu.edu.eg
Abstract: In this talk, optimal control of a general nonlinear multi-strain tuberculosis (TB) model that incorporates three strains drug-sensitive, emerging multi-drug resistant and extensively drug-resistant is presented. The general multi-strain TB model is introduced as a fractional order multi-strain TB model. The fractional derivatives are described in the Caputo sense. An optimal control problem is formulated and studied theoretically using the Pontryagin maximum principle. Four controls variables are proposed to minimize the cost of interventions. Two simple-numerical methods are used to study the nonlinear fractional optimal control problem. The methods are the iterative optimal control method and the generalized Euler method. Comparative studies are implemented, and it is found that the iterative optimal control method is better than the generalized Euler method.
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Title:A Survey and recent contributions on Oscillation of second order dynamic equations on time scales
Author Information
Name:M.M.A.El-Sheikh
University/Institute:Faculty of Science, Menoufia University, Shebeen El-Koom, Egypt
Email:msheikh_1999@yahoo.com
Abstract: The present talk deals with a survey on the oscillation and nonoscillation of solutions of second order dynamic equations on time scales developed by numerous researchers in a chronological order as the field developed year after year from 1990. Firstly we give some known results in different classes of linear and nonlinear dynamic equations, then a lot of reaearchs material related to the series of contributions in the oscillation of several classes of dynamic equations followed by recent extensions and ideas. We finally introduce our recent contributions published in 2015 and other accepted works in 2016. At the end we give some illustrative examples to justify some of the recent results.
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Title:The Shrinking of Gas Bubbles in the Bio tissues between Two-Phase Flow under the effect of Suction and Injection Processes
Author Information
Name:Selim Ali Mohammadein
University/Institute:Tanta University, Faculty of Science
Email:selimali40_43@yahoo.com
First Additional Author Information
Name:Asmaa Elhabshi
University/Institute:Tanta
Email:selimali2009@yahoo.com
Abstract: The effects of suction and injection processes on the collapsing of Nitrogen gas bubbles with constant ambient pressure are obtained. The mathematical model is formulated by Fick, and concentration equations and then solved by analytical method. The collapse of gas bubbles is affected by tissue concentration diffusivity and void fraction. The suction process peforms lower values of shrinking than injection. Results showed that, the suction process activates the systemic blood circulation and accelerate the collapsing of gas bubbles in the bio tissues to avoid the incidence of decompression sickness (DCS).
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Title:A fractional order network model for ZIKA
Author Information
Name:E.Ahmed
University/Institute:Mansoura Faculty of science, math dept.
Email:magd54@gmail.com
First Additional Author Information
Name:Hala Elsaka
University/Institute:Damietta faculty of science, Math dept.
Email:halaelsaka@yahoo.com
Abstract: Zika is a fast spreading epidemic. So far it is known to have two transmission routes one via mosquito and the other is via sexual contact. It is dangerous on pregnant women otherwise it is mild or asymptomatic. Therefore we present a fractional order network model for it
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Title:Modified exponential Chebyshev operational matrices of derivatives for solving high-order partial differential equations in unbounded domains
Author Information
Name:Mohamed A. Abd El Salam
University/Institute:Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, EGYPT
Email:mohamed_salam1985@yahoo.com
First Additional Author Information
Name:Mohamed A. Ramadan
University/Institute:Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, EGYPT
Email:ramadanmohamed13@yahoo.com
Second Additional Author Information
Name:Kamal R. Mohamed
University/Institute:Mathematics Department, Faculty of Science, Al-Azhar University, Cairo, EGYPT
Email:kamal_raslan@yahoo.com
Third Additional Author Information
Name:Talaat S. El Danaf
University/Institute:Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, EGYPT
Email:talaat11@yahoo.com
Abstract: In this paper, a modified type of exponential Chebyshev operational matrices of derivatives is presented. The introduced operational matrices employed for solving high-order linear partial differential equations (PDEs) with variable coefficients under general form of conditions by collocation method. The method based on the approximation by the truncated double exponential Chebyshev (EC) series. The PDEs and conditions are transformed into block matrix equations, which correspond to a system of linear algebraic equations with the unknown EC coefficients, by using EC collocation points. Combining these matrix equations and then solving the system yields the EC coefficients of the solution function. Numerical examples are included to demonstrate the validity and applicability of the method.
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Title:SOLVING JOB_SHOP SCHEDULING PROBLEMS USING HYBRID GENETIC ALGORITHM
Author Information
Name:Sarah Mohammed Nasr
University/Institute:Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom,Menoufia University, Egypt
Email:sarah.nasr.eid@gmail.com
First Additional Author Information
Name:M. A. El-Shorbagy
University/Institute:Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom,Menoufia University, Egypt
Email:mohammed_shorbagy@yahoo.com
Second Additional Author Information
Name:I. M. El-Desoky
University/Institute:Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom,Menoufia University, Egypt
Email:eldesokyi@yahoo.com
Third Additional Author Information
Name: A. A. Mousa
University/Institute:Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom,Menoufia University, Egypt
Email:a_mousa15@ yahoo.com
Forth Additional Author Information
Name:Z. M. HendawyI
University/Institute:Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom,Menoufia University, Egypt
Email:zhendawy2010@yahoo.com
Abstract: Job Shop Scheduling Problem (JSSP) is an optimization problem in which ideal jobs are assigned to resources at particular times. In recent years many attempts have been made at the solution of this problem using a various range of tools and techniques. This paper presents a hybrid genetic algorithm (GA) for JSSP. The hybrid algorithm is a combination between genetic algorithm and local search. Firstly, a generation alternation model using GA is designed. A new initialization method is proposed. Advanced crossover and mutation operators are used. Then local search based on the neighborhood structure is applied in the GA result. The approach is tested on a set of standard instances taken from the literature. The computation results have validated the effectiveness of the proposed algorithm. KEYWORDS: Genetic algorithm, Job shop scheduling problem, Local search
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