Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69776120160201A Linearization Technique for Optimal Design of the Damping Set with Internal Dissipationیک روش خطی برای طراحی بهینه چشمه میرایی دارای اتلاف داخلی1312445710.22067/ijnao.v6i1.44335ENA. Fakharzadeh J.Department of Mathematics, Faculty of Mathematics, Shiraz University of Technology, Shiraz, Iran.H. Alimorad D.Department of Mathematics, Jahrom University, Jahrom, Iran, P. O. Box: 74135-111 Dept. of Mathematics, Shiraz University of Technology, Shiraz , Iran.A. BeiranvandDepartment of Mathematics, Faculty of Mathematics, Shiraz University of Technology, Shiraz, Iran.Journal Article19700101Considering 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.https://ijnao.um.ac.ir/article_24457_56d33b965788e68271663adb83293b17.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69776120160201Chebyshev Galerkin method for integro-differential equations of the second kindروش گالرکین چبیشف برای معادلات انتگرال-دیفرانسیل ازمرتبه دوم31432445910.22067/ijnao.v6i1.37480ENJ. BiazarDepartment of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran.0000-0001-8026-2999F. SalehiDepartment of Mathematics, Darab Branch, Islamic Azad University, Darab, Iran.Journal Article19700101In 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.https://ijnao.um.ac.ir/article_24459_1422a9283f123f7d1214a3e5bd1af1d4.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69776120160201Kudryashov method for exact solutions of isothermal magnetostatic atmospheres43532446110.22067/ijnao.v6i1.45464ENN. KadkhodaDepartment of Mathematics, Faculty of Basic Sciences, Bozorgmehr University Of Qaenat, Qaenat, Iran.H. JafariDepartment of Mathematics and Computer Science,University of Mazandaran, Babolsar, Iran.Journal Article19700101The 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.https://ijnao.um.ac.ir/article_24461_0deef39e37fd196f6824383f14797ee9.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69776120160201A nonstandard finite difference scheme for solving three-species food chain with fractional-order Lotka-Volterra modelیک طرح تفاضلی متناهی غیر استاندارد برای حل شبکه ی غذایی سه بعدی با مدل لوتکا-ولترا مرتبه ی کسری53792446310.22067/ijnao.v6i1.41619ENS. ZibaeiDepartment of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.M. NamjooDepartment of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article19700101In 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.https://ijnao.um.ac.ir/article_24463_b43fe296ad0305b7ef0c9087ab9c0738.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69776120160201An interactive algorithm for solving multiobjective optimization problems based on a general scalarization technique791012446510.22067/ijnao.v6i1.44631ENM. GhaznaviFaculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.M. IlatiFaculty of Mathematics and Computer Science, Amirkabir University of Technology, 424,
Hafez Avenue, 15914 Tehran, Iran.E. KhorramFaculty of Mathematics and Computer Science, Amirkabir University of Technology, 424,
Hafez Avenue, 15914 Tehran, Iran.Journal Article19700101The 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.https://ijnao.um.ac.ir/article_24465_8aae13bf1340a1bcd22a46c738a4e218.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69776120160201A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systemsیک الگوریتم ناحیه اطمینان غیریکنوا با شعاع تطبیقی غیریکنوا برای حل دستگاه معادلات غیر خطی1011212446710.22067/ijnao.v6i1.45607ENK. AminiDepartment of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran.H. EsmaeiliDepartment of Mathematics, Bu-Ali Sina University, Hamedan, Iran.M. KimiaeiDepartment of Mathematics, Asadabad Branch, Islamic Azad University, Asadabad, Iran.Journal Article19700101This 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.https://ijnao.um.ac.ir/article_24467_1ba15f55057e5082b16ff3da82728819.pdfFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69776120160201A contractive mappings on fuzzy normed linear spacesتوابع انقباض روی فضاهای نرم دار فازی1211362447110.22067/ijnao.v6i1.41683ENM. SaheliDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Journal Article19700101In 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.https://ijnao.um.ac.ir/article_24471_313316f842b7e59229f4d7e503dd7d19.pdf