IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION
Year:2016 | Volume:6 | Issue:1 |Papers Count:7

Considering a damped wave system de ned on a two-dimensional domain, with a dissipative term localized in an unknown subset with an unknowndamping parameter, we address the ill-posed shape design problem whichconsists of optimizing the shape of the unknown subset in order to minimizethe energy of the system at a given time. By using a new approach basedon the embedding process,  rst the system is formulated in variational form. Then, by transferring the problem into polar coordinates and de ning twopositive Radon measures, we represent the problem in a space of measures. Hence, the shape design problem is changed into an in nite linear one whosesolution is guaranteed. In this stage, by applying two subsequent approxi-mation steps, the optimal solution (optimal control, optimal region, optimaldamping parameter and optimal energy) is identi ed by a three-phase opti-mization search technique. Numerical simulations are also given in order tocompare this new method with level set algorithm.

In this paper, we propose an efficient implementation of the ChebyshevGalerkin method for  rst order Volterra and Fredholm integro-differentialequations of the second kind. Some numerical examples are presented toshow the accuracy of the method.

The Kudryashov method to look for the exact solutions of the nonlineardifferential equations is presented. The Kudryashov method is applied tosearch for the exact solutions of the Liouville equation and the Sinh-Poissonequation. The equations of magnetohydrostatic equilibria for a plasma in agravitational  eld are investigated analytically. An investigation of a familyof isothermal magnetostatic atmospheres with one ignorable coordinate cor-responding to a uniform gravitational  eld in a plane geometry is carried out. The distributed current in the model J is directed along the x-axis where xis the horizontal ignorable coordinate. These equations transform to a singlenonlinear elliptic equation for the magnetic vector potential u. This equationdepends on an arbitrary function of u that must be speci ed.

In this paper, we introduce fractional-order for a model of tritrophic foodchain Lotka-Volterra. Moreover, we discuss the stability analysis of fractionalsystem. The nonstandard  nite difference (NSFD) scheme is implemented tostudy the dynamic behaviors in the fractional-order Lotka-Volterra system. Numerical results show that the NSFD approach is easy to implement andaccurate when applied to fractional-order Lotka-Volterra system.

The wide variety of available interactive methods brings the need for cre-ating general interactive algorithms enabling the decision maker (DM) toapply freely several convenient methods which best  t his/her preferences. To this end, in this paper, we propose a general scalarizing problem for multi-objective programming problems. The relation between optimal solutions ofthe introduced scalarizing problem and (weakly) efficient as well as properlyefficient solutions of the main multiobjective optimization problem (MOP) isdiscussed. It is shown that some of the scalarizing problems used in differentinteractive methods can be obtained from proposed formulation by selectingsuitable transformations. Based on the suggested scalarizing problem, wepropose a general interactive algorithm (GIA) that enables the DM to spec-ify his/her preferences in six different ways with capability to change his/herpreferences any time during the iterations of the algorithm. Finally, a numer-ical example demonstrating the applicability of the algorithm is provided.

This paper presents a trust-region procedure for solving systems of non-linear equations. The proposed approach takes advantages of an effectiveadaptive trust-region radius and a nonmonotone strategy by combining bothof them appropriately. It is believed that selecting an appropriate adaptiveradius based on a suitable nonmonotone strategy can improve the efficiencyand robustness of the trust-region framework as well as can decrease the com-putational cost of the algorithm by decreasing the number of subproblemsthat must be solved. The global convergence to  rst order stationary pointsas well as the local q-quadratic convergence of the proposed approach areproved. Numerical experiments show that the new algorithm is promisingand attractive for solving nonlinear systems.

In this paper, we use the de nition of fuzzy normed spaces given byBag and Samanta and provide four types of fuzzy versions of contraction. We show that these mappings necessarily have unique  xed points in fuzzynormed linear spaces. Moreover we prove that the presented theorems areindeed fuzzy extensions of their classical counterparts.