Iranian Journal of Numerical Analysis and Optimization
Volume:4 Issue: 2, Summer and Autumn 2014

This 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.

In 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.

In 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.

This 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.

A 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.

In 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.