A Linearization Technique for Optimal Design of the Damping Set with Internal Dissipation
A.
Fakharzadeh J.
Department of Mathematics, Faculty of Mathematics, Shiraz University of Technology, Shiraz, Iran.
author
H.
Alimorad D.
Department of Mathematics, Jahrom University, Jahrom, Iran, P. O. Box: 74135-111 Dept. of Mathematics, Shiraz University of Technology, Shiraz , Iran.
author
A.
Beiranvand
Department of Mathematics, Faculty of Mathematics, Shiraz University of Technology, Shiraz, Iran.
author
text
article
2016
eng
Considering a damped wave system defined on a two-dimensional domain, with a dissipative term localized in an unknown subset with an unknown damping parameter, we address the shape design ill-posed problem which consists of optimizing the shape of the unknown subset in order to minimize the energy of the system at a given time. By using a new approach based on the embedding process, first, the system is formulated in variational form; then, by transferring the problem into polar coordinates and defining two positive Radon measures, we represent the problem in a space of measures. In this way, the shape design problem is changed into an infinite linear one whose solution is guaranteed. In this stage, by applying two subsequent approximation steps, the optimal solution (optimal control, optimal region, optimal damping parameter and optimal energy) is identified by a three-phase optimization search technique. Numerical simulations are also given in order to compare this new method with another one.
Iranian Journal of Numerical Analysis and Optimization
Ferdowsi University of Mashhad
2423-6977
6
v.
1
no.
2016
1
31
https://ijnao.um.ac.ir/article_24457_56d33b965788e68271663adb83293b17.pdf
dx.doi.org/10.22067/ijnao.v6i1.44335
Chebyshev Galerkin method for integro-differential equations of the second kind
J.
Biazar
Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran.
author
F.
Salehi
Department of Mathematics, Darab Branch, Islamic Azad University, Darab, Iran.
author
text
article
2016
eng
In this paper, we propose an efficient implementation of the Chebyshev Galerkin method for first order Volterra and Fredholm integro-differential equations of the second kind. Some numerical examples are presented to show the accuracy of the method.
Iranian Journal of Numerical Analysis and Optimization
Ferdowsi University of Mashhad
2423-6977
6
v.
1
no.
2016
31
43
https://ijnao.um.ac.ir/article_24459_1422a9283f123f7d1214a3e5bd1af1d4.pdf
dx.doi.org/10.22067/ijnao.v6i1.37480
Kudryashov method for exact solutions of isothermal magnetostatic atmospheres
N.
Kadkhoda
Department of Mathematics, Faculty of Basic Sciences, Bozorgmehr University Of Qaenat, Qaenat, Iran.
author
H.
Jafari
Department of Mathematics and Computer Science,University of Mazandaran, Babolsar, Iran.
author
text
article
2016
eng
The Kudryashov method to look for the exact solutions of the nonlinear differential equations is presented. The Kudryashov method is applied to search for the exact solutions of the Liouville equation and the Sinh-Poisson equation. The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. An investigation of a family of isothermal magnetostatic atmospheres with one ignorable coordinate cor-responding to a uniform gravitational field in a plane geometry is carried out. The distributed current in the model J is directed along the x-axis where x is the horizontal ignorable coordinate. These equations transform to a single nonlinear elliptic equation for the magnetic vector potential u. This equation depends on an arbitrary function of u that must be specified.
Iranian Journal of Numerical Analysis and Optimization
Ferdowsi University of Mashhad
2423-6977
6
v.
1
no.
2016
43
53
https://ijnao.um.ac.ir/article_24461_0deef39e37fd196f6824383f14797ee9.pdf
dx.doi.org/10.22067/ijnao.v6i1.45464
A nonstandard finite difference scheme for solving three-species food chain with fractional-order Lotka-Volterra model
S.
Zibaei
Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
author
M.
Namjoo
Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
author
text
article
2016
eng
In this paper, we introduce fractional-order for a model of tritrophic food chain Lotka-Volterra. Moreover, we discuss the stability analysis of fractional system. The nonstandard finite difference (NSFD) scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Numerical results show that the NSFD approach is easy to implement and accurate when applied to fractional -order Lotka-Volterra system.
Iranian Journal of Numerical Analysis and Optimization
Ferdowsi University of Mashhad
2423-6977
6
v.
1
no.
2016
53
79
https://ijnao.um.ac.ir/article_24463_b43fe296ad0305b7ef0c9087ab9c0738.pdf
dx.doi.org/10.22067/ijnao.v6i1.41619
An interactive algorithm for solving multiobjective optimization problems based on a general scalarization technique
m.
Ghaznavi
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.
author
M.
Ilati
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424,
Hafez Avenue, 15914 Tehran, Iran.
author
E.
Khorram
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424,
Hafez Avenue, 15914 Tehran, Iran.
author
text
article
2016
eng
The wide variety of available interactive methods brings the need for creating general interactive algorithms enabling the decision maker (DM) to apply freely several convenient methods which best fit his/her preferences. To this end, in this paper, we propose a general scalarizing problem for multiobjective programming problems. The relation between optimal solutions of the introduced scalarizing problem and (weakly) efficient as well as properly efficient solutions of the main multiobjective optimization problem (MOP) is discussed. It is shown that some of the scalarizing problems used in different interactive methods can be obtained from proposed formulation by selecting suitable transformations. Based on the suggested scalarizing problem, we propose a general interactive algorithm (GIA) that enables the DM to specify his/her preferences in six different ways with capability to change his/her preferences any time during the iterations of the algorithm. Finally, a numerical example demonstrating the applicability of the algorithm is provided.
Iranian Journal of Numerical Analysis and Optimization
Ferdowsi University of Mashhad
2423-6977
6
v.
1
no.
2016
79
101
https://ijnao.um.ac.ir/article_24465_8aae13bf1340a1bcd22a46c738a4e218.pdf
dx.doi.org/10.22067/ijnao.v6i1.44631
A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systems
K.
Amini
Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran.
author
H.
Esmaeili
Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran.
author
M.
Kimiaei
Department of Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran.
author
text
article
2016
eng
This paper presents a trust-region procedure for solving systems of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region framework as well as can decrease the computational cost of the algorithm by decreasing the number of subproblems that must be solved. The global convergence to first order stationary points as well as the local q-quadratic convergence of the proposed approach are proved. Numerical experiments show that the new algorithm is promising and attractive for solving nonlinear systems.
Iranian Journal of Numerical Analysis and Optimization
Ferdowsi University of Mashhad
2423-6977
6
v.
1
no.
2016
101
121
https://ijnao.um.ac.ir/article_24467_1ba15f55057e5082b16ff3da82728819.pdf
dx.doi.org/10.22067/ijnao.v6i1.45607
A contractive mappings on fuzzy normed linear spaces
M.
Saheli
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
author
text
article
2016
eng
In this paper, we use the definition of fuzzy normed spaces given by Bag and Samanta and provide four types of fuzzy versions of contraction. We show that these mappings necessarily have unique fixed points in fuzzy normed linear spaces. We will show that the presented theorems are indeed fuzzy extensions of their classical counterparts.
Iranian Journal of Numerical Analysis and Optimization
Ferdowsi University of Mashhad
2423-6977
6
v.
1
no.
2016
121
136
https://ijnao.um.ac.ir/article_24471_313316f842b7e59229f4d7e503dd7d19.pdf
dx.doi.org/10.22067/ijnao.v6i1.41683