International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications. .::. Invited Lecture
1
TUE: 29-12-2015 Main Hall Invited Speaker Sec16 ( 1 )
 12:45 : 01:15

NAM - 4 EG Prof. Nasser Sweilam nsweilam@sci.cu.edu.eg

20
An efficient method for solving 2-D fractional Schrödinger equation with the Riesz-Feller derivative
Nasser Hassan Sweilam , Muneer M. Abou Hasan

 Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

ABSTRACT
In this paper, we present an accurate numerical method for solving a space fractional Schrödinger equation in two dimensions. The quantum Riesz-Feller fractional derivative is used to define the fractional derivatives. The weighted average non-standard finite difference method is implemented to study the behavior of the model problem. The stability analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis, moreover the truncation error is analyzed. Some numerical test examples are presented with variety values of derivative order α,1<α≤2 and skewness θ. It is found that the proposed method is easy to implement, effective and convenient for solving the proposed model.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
2
( )
 :

NAM - 18 EG Ms. Omima Abo zaid omima_abdelaty@yahoo.com

20
FREE CONVECTION BOUNDARY LAYER FLOW DUE TO OXYTACTIC MICROORGANISMS ABOVE AN INCLINED PLATE EMBEDDED IN A NON-DARCY POROUS MEDIUM SATURATED BY A NANOFLUID
F.M. Hady1 , R. A. Mohamed , Omima A. Abo zaid , A. Mahdy

 1Department of Mathematics, Faculty of Sciences, Assiut University, Assiut 71515, Egypt 2Department of Mathematics, Faculty of Sciences, South Valley University, Qena 83523, Egypt 2Department of Mathematics, Faculty of Sciences, South Valley University, Qena 83523, Egypt 2Department of Mathematics, Faculty of Sciences, South Valley University, Qena 83523, Egypt

ABSTRACT
Free convection flow with heat and mass transfer of a water-based nanofluid containing nanoparticles and motile microorganisms over a semi-infinite inclined flat plate embedded in a non Darcy porous medium is investigated numerically. The partial differential equations (PDEs) are transformed to nonlinear ordinary differential equations (NODEs) using similarity transformations, which are then solved numerically using fourth-order Runge–Kutta method. Both Brownian motion and thermophoresis effects are incorporated into the nanfluid model. The effect of inclination angle on the flow is tested. Also the effects of the governing parameters on the dimensionless quantities like velocity, temperature, nanoparticle concentration, density of motile microorganisms, local Nusselt, local Sherwood and local density numbers for both nanoparticles and motile microorganism density are explored. From this extensive study, it is found that the dimensionless velocity decreases near the wall with an increase in the inclination angle and bioconvection Rayleigh number, but the opposite behavior become clear to stay away from the wall, in addition to the dimensionless temperature increases with increasing bioconvection Rayleigh number and the inclination angle. It is also found that nanofluid and bioconvection parameters have strong effects on local Nusselt, Sherwood and density numbers.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
3
( )
 :

NAM - 19 NG Assoc.Prof. Ogungbe Oluwasegun Kelvin federaluniversitytechnologymin@gmail.com

20
COMPUTER SCIENCE AND DEVELOPMENT PROGRAMMING

 Computer Management COMPUTER MANAGEMENT & MENTAINANCE COMPUTER SCIENCE PROGRAMMING

ABSTRACT
PROJECT THE FOR COMPUTER SCIENCE COURSE PROJECT MAN- AGEMENT Department of Computer Science & Technology Federal University of Technology Nigeria. Minna - Zungeru Rd, Minna,Nigeria,1983 +2340903 849 1766 federaluniversitytechnologymin@gmail.com ABSTRACT Project-based assignments are widely used in Computer Science courses to give students hands-on experience in using the learned knowledge to solve problems. However, despite its importance, management on student projects is usually done in an ad-hoc fashion, with varying degrees of interaction and guidance to students. This paper presents a general, Wiki-based project management framework: project activities are centralized and captured by a dedicated Wiki site, consisting of Wiki pages created by both the instructor and students. The Project Wiki framework supports all types of project activities, and enables flexible and multi-dimension interaction patterns for instructor, individual student and the whole class. INTRODUCTION Project-based assignments have been widely used in Computer Science courses [2, 11, 10]; in fact, most recently published CS textbooks include companion web sites offering course project materials, for example, see [7, 4]. By doing course projects, students deepen their understanding on course subject matter and gain hands-on experience in using their learned knowledge to solve problems — the main goal in active learning. However, despite its importance, management on student projects is usually done in an ad-hoc fashion: instructors use different tools and techniques, specific to a particular course or instructor, with varying degrees of interaction and guidance to students. To address these issues, this paper presents a general, Wiki-based project management framework which can be easily modified and used in typical computer science courses. Using Project Wiki, project activities are centralized and captured by a dedicated Wiki site, consisting of Wiki pages created by both the instructor and students. Instructors create template pages to guide student through projects and highlight key requirements; students create and maintain their own Wiki pages for project planning and logging; instructors review student pages to check project status and give feedback; students can also review and add comments to each other’s Wiki; finally, the whole class can access and edit common group Wiki pages to engage in broader community-style collective learning. The contributions of this paper are the following: • we developed a general and flexible Wiki-based project management framework; • we present the structure and setup of the Project Wiki framework, and explore enabled activities; • we describe our experience using it in a project-oriented compiler class. The rest of the paper is organized as follows: Section 2 describes the background and motivation of Wiki-based project management; Section 3 describes the Project Wiki framework, and the users, activities, and typical settings. Section 4 presents our experience using Project Wiki in a project-oriented compiler class. We conclude in Section 5.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
4
( )
 :

NAM - 20 EG Dr. Iman Ibrahim imanhfz.asa@gmail.com

20
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ABSTRACT
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 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
5
SUN: 27-12-2015 Hall[B] Oral - Sec02 ( 1 )
 03:15 : 03:30

NAM - 2 NG Dr. MORUFU OYEDUNSI OLAYIWOLA olayiwola.oyedunsi@uniosun.edu.ng

20
On the Efficiency of Modified Variational Iteration Method for the Solution of a Class of Nonlinear Partial Differential Equation
Dr. Morufu Oyedunsi OLAYIWOLA

 Department of Mathematical & Physical Sciences, Osun State University, Osogbo, Nigeria.

ABSTRACT
In this paper, a Modified Variational Iteration Method is discussed. Typical application to some nonlinear partial differential equations is presented. The results show a rapid convergent of the method with less iteration and without linearization.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
6
SUN: 27-12-2015 Hall[B] Oral - Sec02 ( 2 )
 03:30 : 03:45

NAM - 5 GB Ms. Doaa Elsakout doaa.elsakout@pet.hw.ac.uk

20
Multilevel Hamiltonian Monte Carlo for Quantifying Uncertainty in Reservoir Simulation
Doaa Elsakout , Mike Christie , Gabriel Lord

 Heriot-Watt University Heriot-Watt University Heriot-Watt University

ABSTRACT
Uncertainty quantification is an important task in reservoir simulation. The main idea of uncertainty quantification is to compute the distribution of a quantity of interest, for example field oil production rate (FOPR). This uncertainty then feeds into the decision making process. A statistically valid way of quantifying the uncertainty is by a Markov Chain Monte Carlo (MCMC) method, such as Metropolis-Hastings (Standard MCMC). Standard MCMC can be prohibitively expensive when the function evaluations take a long time, as in the case of reservoir simulation. Hamiltonian Monte Carlo accelerates the convergence of Standard MCMC, but may lead to a large increase in computational cost because it requires the gradient. In this paper, we present a new way to accelerate convergence for MCMC called Multilevel Hamiltonian Monte Carlo (MLHMC). The idea behind the MLHMC technique is a simple telescoping sum which represents the quantity of interest (e.g. the mean), on the finest grid in terms of the same quantity on a coarse grid plus a series of corrections. First, numerous cheap Hamiltonian Monte Carlo realizations are run on the coarse grid. A small fraction of realizations are then run on the finer grids to compute correction terms. This reduces the computational cost and simulation errors significantly. MLHMC is a combination of the Multilevel Monte Carlo method with a Hamiltonian Monte Carlo algorithm. MLHMC has been implemented on a two real fields called Teal South and Scapa to assess the uncertainty. We show that (a) MLHMC get the same p-quantiles as Hamiltonian Monte Carlo within the sampling error, (b) MLHMC is significantly faster than Hamiltonian Monte Carlo and decreases the computational cost for HMC. Also, we show how the choice of the experimental design affects the solution.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
7
SUN: 27-12-2015 Hall[B] Oral - Sec02 ( 3 )
 03:45 : 04:00

NAM - 6 EG Mr. Adel A. El-Sayed aaa18@fayoum.edu.eg

20
Solving Time-Fractional Order Telegraph Equation Via Sinc-Legendre Collocation Method
N. H. Sweilam , A. M. Nagy , Adel A. El-Sayed

 Departement of mathematics, Faculty of science, Cairouniversity Departement of mathematics, Faculty of science, Banha university Departement of mathematics, Faculty of science, Fayoum university

ABSTRACT
In this paper, We introduce a numerical method for solving fractional order telegraph equation. The method depends basically on the fact that an expansion of approximated solution in a series of Sinc function and shifted Legendre polynomials. The fractional derivative is expressed in the Caputo definition of fractional derivatives. The expansion coefficients are then determined by reducing the time fractional order telegraph equation with its boundary and initial conditions to a system of a algebraic equations for these coefficients. This system may be solved numerically by using the Newton's iteration method. Several numerical examples are introduced to demonstrate the reliability and effectiveness of the introduced method.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
8
SUN: 27-12-2015 Hall[B] Oral - Sec02 ( 4 )
 04:00 : 04:15

NAM - 7 EG Dr. Hany Hassan h_nasr77@yahoo.com

20
Single and Dual Solutions of Fractional Order Differential Equations Based on Modified VIM and Simpson Rule

 aDepartment of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, Egypt aDepartment of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, Egypt Engineering Mathematics and Physics Department, Cairo University, 12613, Egypt. Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt.

ABSTRACT
An efficient method is proposed for solving fractional differential equations with strongly terms like (exp, sin, cos,…). The proposed method uses a combination of variational iteration method (VIM) with an auxiliary parameter and Simpson rule. This method effectively applies to Bratu problem in fractional order domain to predict and calculate all branches of problem solutions simultaneously. The proposed approach is also tested on other fractional differential equations. The results demonstrate reliability, simplicity and efficiency of the approach developed.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
9
SUN: 27-12-2015 Hall[B] Oral - Sec02 ( 5 )
 04:15 : 04:30

NAM - 8 AE Prof. Fathalla Rihan frihan@uaeu.ac.ae

20
Mono-Implicit Runge Kutta Method for Singularly Perturbed Delay Differential Equations
Fathalla A. Rihan

 Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, 15551, UAE

ABSTRACT
In this paper, we provide unconditionally stable method based on mono-implicit Runge-Kutta schemes for numerical approximations of singularly perturbed stiff delay differential equations. Numerical Stability analysis is also investigated. The schemes are suitable for both stiff and non-stiff initial value problems. Numerical simulations are provided to show the effectiveness of the methods for stiff problems.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
10
SUN: 27-12-2015 Hall[B] Oral - Sec02 ( 6 )
 04:30 : 04:45

NAM - 9 AE Prof. Fathalla Rihan frihan@uaeu.ac.ae

20
Delay differential model of tumor-immune system with Immuno-Chemotherapy and optimal Control
Fathalla A. Rihan

 Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, 15551, UAE

ABSTRACT
A delay differential model with optimal control is presented to describe the dynamics of tumour-immune interactions in the presence of immuno-chemotherapy treatments. The role of interleukin-2 (IL-2) in stimulation of the effector cells and tumour dynamics is considered in the model with a discrete time-delay to justify the time required to stimulate the effector cells. An expression for the length of the time-delay to preserve stability is deduced. Two optimal control variables are incorporated to identify the best treatment strategy with minimum side effects by blocking the production of new tumour cells and keeping the level of normal cells above the average of its carrying capacity. %Existence of the optimal controls and optimality system are established. Pontryagin's maximum principle is applicable to characterize the optimal controls. An algorithm, to approximate the solution of the optimal control problem, is suggested by solving the state system (forward) and adjoint system (backward) in time. The numerical simulations show that combination therapy protocol of immuno-chemotherapy reduces the tumour cells load in few months of therapy.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
11
SUN: 27-12-2015 Hall[B] Oral - Sec02 ( 7 )
 04:45 : 05:00

NAM - 10 EG Dr. Abdelraheem Mahmoud Aly Abdallah abdelreheam.abdallah@sci.svu.edu.eg

20
Simulations of Fluid-Structure Interactions with Complex Free Surface Flows using an Incompressible Smoothed Particle Hydrodynamics
Abdelraheem Mahmoud Aly Abdallah

 Assistant Professor in Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt

ABSTRACT
In this study, we simulated fluid-structure interaction (FSI) with complex free surface flows using Incompressible Smoothed Particle Hydrodynamics (ISPH) method in two and three dimensions. The governing equations are discretized and solved using ISPH method. In the current algorithm of ISPH method, the pressure was evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection scheme to ensure divergence free velocity field and density invariance condition. In addition, we improved the boundary treatment between the moving rigid body and surrounding fluid. The motions of a rigid body have been computed by direct integration of fluid pressure at the position of each particle on the body surface. The equations of translational and rotational motions were integrated in time to update the position of the rigid body at each time step. In this study, an. The force exerted on the moving rigid boundary particles by the particles surrounding it is calculated by SPH approximation. The applicability and efficiency of current ISPH method are tested by comparison with reference experimental results.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
12
SUN: 27-12-2015 Hall[B] Oral - Sec02 ( 8 )
 05:00 : 05:15

NAM - 17 EG Dr. Amr Mahdy amr_mahdy85@yahoo.com

20
Numerical solution of fractional integro-diff erential equations by least squares method and shifted Chebyshev polynomials of the third kind method
K. R. Mohamed1 , A. M. S. Mahdy , E. M. H. Mohamed3

 ;3 Department of Mathematics, Faculty of Science, Alazhar University, Cairo, Egypt Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt ;3 Department of Mathematics, Faculty of Science, Alazhar University, Cairo, Egypt

ABSTRACT
In this paper, an implementation of an efficient numerical method of linear fractional integro-di fferential equations by least squares method with aid of shifted Chebyshev polynomials of the third kind method. The fractional derivative is described in the Caputo sense. The method is based upon shifted Chebyshev polynomials of the third kind approximations is introduced. Some numerical examples are presented to illustrate the theoretical results and compared with the results obtained by other numerical methods. We have computed the numerical results using Mathematica 9 programming.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
13
MON: 28-12-2015 Hall[B] Oral - Sec05 ( 1 )
 09:00 : 09:15

NAM - 11 EG Dr. nermein abd el-satar engnermeinn@hotmail.com

20
A Matrix Iterative Techniqe for The Solution of Fredholm Integral Equations of The Second Kind
Nermein.A.Saber , Shoukralla.E.S , El-Serafi.S.A

 teaching assistant at BUC university head of mathematic department at Future university proffessor of mathematics, Menofia university

ABSTRACT
A matrix iterative algorithm is given for the approximate solution of fredholm Integral equations of the second kind. Tve algorithm modifies the ideas of the iterated kernel via Hilbert matrix. Thus reducing the required solution so that only one coefficient matrix is computed.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
14
MON: 28-12-2015 Hall[B] Oral - Sec05 ( 2 )
 09:15 : 09:30

NAM - 12 EG Assoc.Prof. Abdallah Aboutahoun tahoun44@yahoo.com

20
An improved upper bounds for the sum of the eigenvalues of some trees
Abdallah W. Aboutahoun , Fatma A. El-Safty

 Associative Professor, Department of Mathematics, Faculty of Science, Alexandria University Assistant Lecturer, Department of Mathematics, Faculty of Science, Damanhour University

ABSTRACT
Let G =(V,E) be a simple connected graph with n and |E| edges. The Laplacian matrix of the graph G is defined by L(G)=D(G)-A(G), where D(G) and A(G) denote the diagonal matrix of vertex-degrees and the adjacency matrix of G, respectively. Let S_k (G) be the sum of the largest k eigenvalues of L(G). In this paper, we study the Laplacian spectrum of trees. We give an improved upper bounds on S_k (T) for some trees T, where it is proved in literature that S_k (T)≤|E|+2k-1 for any tree T.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
15
MON: 28-12-2015 Hall[B] Oral - Sec05 ( 3 )
 09:30 : 09:45

NAM - 13 EG Prof. Mahmoud Annaby mhannaby@sci.cu.edu.eg

20
Exact Computations of Trigonometric Sums by Hermite Interpolation
Mahmoud Annaby , Hassan A. Hassan

 Cairo University Cairo University

ABSTRACT
We use Hermite interpolation formula to derive closed forms for some trigonometric sums. The used nodes are the zeros of Chebyshev polynomials of first and second kinds. We show that some of the resulting formulas are integral valued and we give asymptotic formulas.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
16
MON: 28-12-2015 Hall[B] Oral - Sec05 ( 4 )
 09:45 : 10:00

NAM - 14 EG Ms. Doaa Gamal do3a_g@hotmail.com

20
Comparitve Studies for the Fractional Optimal Control in Transmission Dynamics of West Nile Virus
D. G. Mohamed , N. H. Sweilam , O. M. Saad

 Department of Mathematics, Faculty of Science, Helwan University Department of Mathematics, Faculty of Science, Cairo University Department of Mathematics, Faculty of Science, Helwan University

ABSTRACT
In this paper, numerical studies for the nonlinear fractional-order optimal control problem (FOCP) for the transmission dynamics of West Nile Virus (WNV) are presented. Two numerical methods are used to study the FOCP. The methods are, the iterative optimal control method (IOCM) and the generalized Euler method (GEM). The fractional derivatives are described in the Caputo sense. Pontryagin's maximum principle is applied to solve this FOCP, where the optimality system is composed of nine nonlinear ordinary di erential equations (NODES). Comparative studies are presented, it can be concluded that IOCM is better than GEM.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
17
MON: 28-12-2015 Hall[B] Oral - Sec05 ( 5 )
 10:00 : 10:15

NAM - 15 EG Dr. Amr Mahdy amr_mahdy85@yahoo.com

20
Numerical Study for the Fractional Optimal Control Problem Using Different Method
A. M. S. Mahdy , A. A. H. Mtawa

 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

ABSTRACT
In this paper, we presents an numerical method for solving a class of fractional optimal control problems (FOCPs). The fractional derivative in these problems is in Caputo sence. We obtain the approximate solutions for fractional optimal control of linear systems, which have a quadratic performance index. Using the homotopy Perturbation Sumudu transform method (HPSTM) and Picard method (PM) are applied for solving the extreme conditions obtained from the Pontryagins maximum principle. We construct a fractional optimal feedback contol law. The ressults reveal that the proposed methods are very effiective and simple.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
18
MON: 28-12-2015 Hall[B] Oral - Sec05 ( 6 )
 10:15 : 10:30

NAM - 16 EG Dr. Amr Mahdy amr_mahdy85@yahoo.com

20
Shifted Chebyshev polynomials of the third kind solution for the multi-order nonlinear fractional di erential equations
A. M. S. Mahdy , R. T. Shwayyea2

 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt 2Department of Mathematics, Faculty of Science, Al-Qadisiyah University, Iraq

ABSTRACT
In this paper, an efficient numerical method for solving the multi-order nonlinear fractional di fferential equations (NFDEs) is considered. The fractional derivative is described in the Caputo sense. The method is based upon shifted Chebyshev polynomials of the third kind approxima- tions. The properties of shifted Chebyshev polynomials of the third kind approximations are utilized to reduce multi-order NFDEs to a system of nonlinear of algebraic equations, which solved by the well known method, Newton method. Numerical simulation of multi-order NFDEs is presented and the results are compared with the traditional methods, variational iteration method and the homotopy perturbation method.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
19
MON: 28-12-2015 Hall[B] Oral - Sec05 ( 7 )
 10:30 : 10:45

NAM - 3 EG Prof. El-Sayed Mostafa emostafa@alex-sci.edu.eg

20
On the Solution of a Nonlinear Semidefinite Programming Problem Arising in Discrete-Time Output Feedback Design
El-Sayed M.E. Mostafa , Abdallah Aboutahoun , Fatma F.S. Mohamed

 Professor, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University. Associate Professor, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University.Abdallah Aboutahoun Ph.D. Student, Department of Mathematics and Computer Science, Faculty of Science, Alexandria University.

ABSTRACT
In this paper some nonlinear semi-definite programming problem is considered, which represents the ${\cal H}_\infty$--synthesis problem for discrete-time systems. Two numerical methods are presented for tackling this problem. The first one is a modified Lagrangian method while the second is an augmented Lagrangian method. The difficulty of finding a starting feasible point of the numerical methods with respect to the positive definite constraints of the problem is handled by solving an eigenvalue assignment problem. The two methods are tested numerically on wide range of test problems from the literature.

 International Conference for Mathematics and Applications (ICMA15) Academy of Scientific Research and Technology 27 – 29 DEC. 2015 Cairo, Egypt
المؤتمر الدولي في الرياضيات
(ICMA15)وتطبيقاتها
أكاديمية البحث العلمي والتكنولوجيا
 2015 ديسمبر 29 - 27
القاهرة  ـ  جمهورية مصر العربية

 www.asrt.sci.eg  -  ncm-eg.org ICMA15.msa.edu.eg www.msa.edu.eg

Numerical Analysis Methods and Applications.
20
MON: 28-12-2015 Poster - Sec 01 ( 4 )
 11:30 : 12:15

NAM - 1 DZ Dr. Mohamed El Amine Bencheikh Le Hocine amine_ed@yahoo.fr

20
On finite element approximation in the L^{∞}-norm of system of parabolic quasi variational inequalities
Mohamed el Amine BENCHEIKH LE HOCINE

 Tamanghasset University Centre, Algeria

ABSTRACT
This paper deals with the numerical analysis of system of parabolic quasi variational inequalities related to stochastic control problems. An optimal L^{∞}-convergence of a piecewise linear finite element method is established using the concept of subsolution and discrete regularity.