Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69774220141101Analysing panel flutter in supersonic flow by Hopf bifurcation1142443110.22067/ijnao.v4i2.32430ENZ. MonfaredDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Z. DadiDepartment of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran.0000-0002-4288-1956Journal Article19700101This paper is devoted to study of a partial differential equation governing panel motion in supersonic flow. This PDE can be transformed to an ODE by means of a Galerkin method. Here by using a criterion which is closely related to the Routh-Hurwitz criterion, we investigate the mentioned transformed ODE from Hopf bifurcation point of view. In fact we obtain a region for existence of simple Hopf bifurcation for it. With the aid of computer language Matlab and Hopf bifurcation tool, flutter and limit cycle oscillations of panel are verified. Moreover, Hopf bifurcation theory is used to analyse the flutter speed of the system.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69774220141101Hopf bifurcation in a general n-neuron ring network with n time delays15302443210.22067/ijnao.v4i2.40227ENE. JavidmaneshDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.M. KhorshidiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article19700101In this paper, we consider a general ring network consisting of n neurons and n time delays. By analyzing the associated characteristic equation, a classification according to n is presented. It is investigated that Hopf bifur-cation occurs when the sum of the n delays passes through a critical value.In fact, a family of periodic solutions bifurcate from the origin, while the zero solution loses its asymptotically stability. To illustrate our theoretical results, numerical simulation is given.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69774220141101Population based algorithms for approximate optimal distributed control of wave equations31412443310.22067/ijnao.v4i2.40230ENA. H. BorzabadiSchool of Mathematics and Computer Science, Damghan University, Damghan, Iran.S. MirassadiSchool of Mathematics and Computer Science, Damghan University, Damghan, Iran.M. HeidariSchool of Mathematics and Computer Science, Damghan University, Damghan, Iran.Journal Article19700101In this paper, a novel hybrid iterative scheme to find approximate optimal distributed control governed by wave equations is considered. A partition of the time-control space is considered and the discrete form of the problem is converted to a quasi assignment problem. Then a population based algorithm, with a finite difference method, is applied to extract approximate optimal distributed control as a piecewise linear function. A convergence analysis is proposed for discretized form of the original problem. Numerical computations are given to show the profciency of the proposed algorithm and the obtained results applying two popular evolutionary algorithms, genetic and particle swarm optimization algorithms.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69774220141101Operational Tau method for nonlinear multi-order FDEs43552443410.22067/ijnao.v4i2.33577ENP. MokhtaryDepartment of Mathematics, Sahand University of Technology, Tabriz, Iran.Journal Article19700101This paper presents an operational formulation of the Tau method based upon orthogonal polynomials by using a reduced set of matrix operations for the numerical solution of nonlinear multi-order fractional differential equations(FDEs). The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of non-linear algebraic equations. Some numerical examples are provided to demonstrate the validity and applicability of the method.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69774220141101A new approach for solving nonlinear system of equations using Newton method and HAM57722443510.22067/ijnao.v4i2.32555ENJ. IzadianDepartment of Mathematics, Faculty of Sciences, Mashhad Branch, Islamic Azad University, Mashhad, Iran.R. AbrishamiDepartment of Mathematics, Faculty of Sciences, Mashhad Branch, Islamic Azad University, Mashhad, Iran.M. JaliliDepartment of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran.Journal Article19700101A new approach utilizing Newton Method and Homotopy Analysis Method (HAM) is proposed for solving nonlinear system of equations. Accelerating the rate of convergence of HAM, and obtaining a global quadratic rate of convergence are the main purposes of this approach. The numerical results demonstrate the efficiency and the performance of proposed approach. The comparison with conventional homotopy method, Newton Method and HAM shows the great freedom of selecting the initial guess, in this approach.Ferdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69774220141101Solving nonlinear Volterra integro-differential equation by using Legendre polynomial approximations73832443610.22067/ijnao.v4i2.34304ENM. GachpazanDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.M. ErfanianDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.0000-0001-8449-9272H. BeigloDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article19700101In this paper, we construct a new iterative method for solving nonlinear Volterra Integral Equation of second kind, by approximating the Legendre polynomial basis. Error analysis is worked using Banach fixed point theorem. We compute the approximate solution without using numerical method. Finally, some examples are given to compare the results with some of the existing methods.