Iranian Journal of Numerical Analysis and Optimization
Volume:3 Issue: 2, Summer and Autumn 2013

In this paper, a bidirectional associative memory (BAM) neural network, which consists of two neurons in the X-layer and three neurons in the Y-layer, with two time delays will be studied. We conclude that under some assumptions, Hopf bifurcation occurs when the sum of two delays passes through a critical value. A numerical example is presented to support our theoretical results.

In this work, by using the particle swarm optimization the electron Raman scattering for square double quantum wells is optimized. For this purpose, by combining the particle swarm algorithm together with the numerical solution procedures for equations, and also the perturbation theory we find the optimal structure that maximizes the electron Raman scattering. Application of this algorithm to the structure of asymmetric double quantum wells shows that the differential cross section of an electron Raman scattering is 1.30390×10⁵ Arb.Units.

In this paper, we introduce an efficient method for solving the quadratic Riccati differential equation. In this technique, combination of Laplace transform and new homotopy perturbation methods (LTNHPM) are considered as an algorithm to the exact solution of the nonlinear Riccati equation. Unlike the previous approach for this problem, so-called NHPM, the present method, does not need the initial approximation to be defined as a power series. Four examples in different cases are given to demonstrate simplicity and effciency of the proposed method.

In this paper, the homotopy perturbation method (HPM) and Elzaki transform is employed to obtain the approximate analytical solution of the Sine Gorden and the Klein Gorden equations. The nonlinear terms can be handled by the use of homotopy perturbation method. The proposed homotopy perturbation method is applied to reformulate the first and the second order initial value problems which leads to the solution in terms of transformed variable, and the series solution that can be obtained by making use of the inverse transformation.

This article deals with a computational algorithmic approach for obtaining the optimal solution of a general free boundary problem governed by an elliptic equation with boundary control and functional criterion. After determining the weak solution of the system, the problem is converted into a variational format. Then, by using some aspects of measure theory, the method characterize the nearly optimal pair of domain and its related optimal control function at the same time. This method has many advantages such as strong linearity, automatic existence theorem and the ability of obtaining global solution. Two sets of numerical examples is also given.

We consider a simple mathematical model that suggests emergence of oscillations in p53 and Mdm2 protein levels in response to stress signal. Intracellular activity of the p53 protein is regulated by a transcriptional target, Mdm2, through a feedback loop. The model is classified in five cases with respect to intersection of nullclines. In each case occurrence(or not) of the limit cycle is investigated.