International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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A penalty method with trust-region mechanism for nonlinear bilevel optimization problem

Bothina Elsobky , Yousria Abo-Elnaga

Department of Mathematics, Faculty of Science, Alexandria University, Egypt.

Department of basic science, Higher Technological Institute, Tenth of Ramadan City , Egypt

ABSTRACT

We present a penalty method with trust-region technique for nonlinear bilevel optimization problem in this paper. This method follows Dennis, El-Alem, and Williamson active set idea and penalty method to transform the nonlinear bilevel optimization problem to unconstrained optimization problem. This method maybe simpler than similar ideas and it does not need to compute a base of the null space. A trust-region technique is used to globalize the algorithm. Global convergence theorem is presented and applications to mathematical programs with equilibrium constraints are given.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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Generation of Pareto optimal solutions for multi-objective optimization problems via a reduced interior-point algorithm

Bothina Elsobky , Yousria Abo-Elnaga

Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Egypt.

Department of basic science, Higher Technological Institute, Tenth of Ramadan City , Egypt

ABSTRACT

In this paper, a reduced interior-point algorithm is introduced to generate a Pareto optimal front for multi-objective constrained optimization (MOCP) problem. A weighted Tchebychev metric (WTM) approach is used together with achievement secularizing function approach to convert (MOCP) problem to a single-objective constrained optimization(SOCO) problem. An active-set technique is used together with a Coleman-Li scaling matrix to find the solution of (SOCO)problem. A decrease interior-point method is used to compute Newton’s step by solving a smaller dimension system.
A Matlab implementation of the proposed algorithm was used to solve three cases and application. The results showed that the algorithm out perform some existing methods in literature. The results, by using our suggested approach to benchmark problems are promising when compared with well-known algorithms. Also, our outcomes recommend that our calculation may be superior relevant for comprehending real-world application problems.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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L∞–error Estimate for an Approximation of asystem of Parabolic Variational Inequalities

HAIOUR MOHAMED , Salah Boulaaras , Mohamed Amine Bencheikh Le Hocine

LANOS Laboratory, Department of Mathematics, Faculty of Sciences, Badji Mokhtar University, Annaba, Algeria

Department of Mathematics, Colleague of Science and Arts, Al-Ras, Al-Qassim University, Kingdom Of Saudi Arabia

Department of Mathematics and Computer Science, Tamanghesset University Center, Sersouf, Tamanghesset , Algeria;

ABSTRACT

In this paper, a system of parabolic quasi-variational inequalities relevant to the management of energy production with mixed boundary condition was considered where a quasi-optimal of error estimate on uniform norm was proved, by using theta scheme combined with Galerkin method. Furthermore, an asymptotic behavior result in the same norm was proved. Taking into consideration the discrete stability properties.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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PERFORMANCE ANALYSIS OF TWO MODIFIED BROYDEN LIKE METHODS FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

Kabiru Muhammad , Abdurrahman Abdulhamid

Department of Statistics, Kano State Polytechnic, Kano Nigeria.

Department of Statistics, Kano State Polytechnic, Kano Nigeria

Department of Statistics, Kano State Polytechnic, Kano Nigeria.

ABSTRACT

Abstract: In this paper an analysis on the performance of two modified Broyden method is presented: Broyden – like Method (BLM) and Trapezoidal Broyden Method (TBM) . Four test problems with standard initial points were used to compare the performance of the two methods in terms of CPU time and Number of Iterations. Numerical results have shown that there is little difference between the two methods in terms of Number of Iterations. Further analysis using performance indices has also shown that TBM is superior to BLM in terms of CPU time.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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NOVEL WENO ALGORITHMS USING UNDIVIDED DIFFERENCES

Tamer Heshmat Mohamed Aly Kasem

Cairo University, Faculty of Engineering

ABSTRACT

A new smoothness indicator (SI) for the high order weighted essentially non oscillatory (WENO) method is introduced. The new SI formula is based on undivided differences (UD), but they improve the original UD WENO scheme by keeping the formal order of accuracy. The new algorithm is tested and compared with the classical WENO algorithm based on total variations. The advantages of the new scheme are clarified.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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Comparative Studies for Solving the General Nonlinear Klein Gordon Model

Nasser Hassan Sweilam , Seham AL-Mekhlai , Anan O. Albalawi

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

Department of Mathematics, Faculty of Education, Sana'a University, Sana'a, Yemen.

Department of Mathematics, Faculty of Science, Shaqra University, Riyadh, Saudi Arabia

ABSTRACT

In this talk, Different numerical techniques are used to study the general nonlinear Klein-Gordon Model. Integer, Fractional, and variable order Klein-Gordon models are introduced. The nonstandard weighted average finite difference method is used to study the proposed model problems. The stability condition and the error estimates of the proposed method are presented. Comparative studies are done. The numerical results are compared with both the explicit standard finite difference method and the nonstandard finite difference method. It is found that the stability regions are bigger using the nonstandard weighted average finite difference method.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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Spectral tau Algorithm for Solving a Class of Fractional Optimal Control Problems via Jacobi Polynomials

Youssri H. Youssri , Waleed M. Abd-Elhameed

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

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

ABSTRACT

This paper is dedicated to analyzing and presenting an efficient numerical algorithm for solving a class of fractional optimal control problems (FOCPs). The basic idea behind the suggested algorithm is based on transforming the FOCP under investigation into a coupled system of fractional-order differential equations whose solutions can be expanded in terms of the Jacobi basis. With the aid of the spectral-tau method, the problem can be reduced into a system of algebraic equations which can be solved via any suitable solver. Some illustrative examples and comparisons are presented aiming to demonstrate the accuracy, applicability, and efficiency of the proposed algorithm.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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الرياضه العدديه وتطورها العقلي لمواجه مشكله صعوبات التعلم الرياضي

احمد الرفاعي فتحي النحراوي

وزاره الشئون الاجتماعيه

ABSTRACT

مشكله صعوبات التعلم
يمكن لبعض المسائل في التحليل العددي أن تحل بشكل دقيق عن طريق خوارزمية ما ويسمى هذا النوع من الخوارزميات "طرقا مباشرة" : مثالها الاختصار الغاوسي لحل جمل المعادلات الخطية وطريقة التبسيط (طريقة سيمبلكس) في البرمجة الخطية.
وهناك ظاهره كبيره في صعوبات التعلم الرياضيه

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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ADVANCED APPROACH FOR MULTI-OBJECTIVE FRACTIONAL PROGRAMMING PROBLEMS

E.A.Youness , N.A.El-Kholy , H.A.Eldidamony

Faculty of Science, Tanta University, Tanta, Egypt

Faculty of Science, Tanta University, Tanta, Egypt

Higher Technological Institute, 10th of Ramadan city, Egypt

ABSTRACT

In this paper, a new approach for finding all efficient solutions for multi-objective fractional programming problems is presented. This approach based on solving auxiliary problems, one of them to obtain minimizing the numerator and the other maximizing the denominator. Illustrative examples are presented to clarify the obtained results.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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Discrete spline Numerov method for solving Swift-Hohenberg equation

W. K. Zahra , S. M. Elkoly

Department of Engineering Physics and Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt and 2Department of Mathematics, Basic and Applied Sciences School, Egypt-Japan University of Science and Technology, New Borg El-Arab City, Alexandria, 21934, Egypt.

Department of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El Sheikh Univ., Egypt

ABSTRACT

Discrete spline function based method is developed to solve the time fractional Swift-Hohenberg equation in the sense of Riemann Liouville derivative. Via Fourier method, the developed method is unconditionally stable. Two schemes are acquired, these schemes are verified to be convergent of order two and four. Numerical results are demonstrated for various values of fractional Brownian as a function of time and also the standard motion to confirm the applicability and the theoretical results.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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On the location of a constrained k-tree facility in a tree network with unreliable edges

Abdallah W . Aboutahoun , Eman Fares

(ِِAssoc. Prof.) Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

(ِِِAssistant teacher)Department of Basic Science, Faculty of Engineering, Pharos University, Alexandria, Egypt

ABSTRACT

Given a tree network T with n vertices where each edge has an independent operational probability, we are interested in finding a subtree with at most k leaves and with a diameter of at most l which maximizes the expected number of nodes that are reachable from the selected subtree by operational paths. An efficient algorithm is presented for finding a (k, l) – tree core of T. Examples are provided to illustrate the algorithm.

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International Conference on Mathematics, Trends and Development ICMTD17 ,

Cairo, Egypt, 28 – 30 Dec. 2017 Organized by The Egyptian Mathematical Society,

Web Site: http://www.etms-eg.org

Numerical Analysis Methods and Applications.

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Bicriteria Tree-Shaped Facility Location Problem on a Tree Network with Median and Center Objectives

Abdallah W. Aboutahoun

Associative Prof., Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

ABSTRACT

As an extension of classical facility location models in network, the problem of locating a tree-shaped facility in a tree network is considered. We consider the minisum criterion in which the sum of the distances from all the vertices of the tree network to the facility is minimized and the minimax criterion in which the distance from the facility to the farthest vertex in the tree network is minimized. Using single criterion does not capture all essential elements of a location problem. An efficient algorithm is developed which generate the set of all Pareto-optimal subtrees in the objective space. Examples are provided to illustrate the algorithm