Journal of Mathematical Modeling
Volume:3 Issue: 1, Spring 2015

In this paper, we study the problem of minimizing the ratio of two quadratic functions subject to a quadratic constraint. First we introduce a parametric equivalent of the problem. Then a bisection and a generalized Newton-based method algorithms are presented to solve it. In order to solve the quadratically constrained quadratic minimization problem within both algorithms, a semidefinite optimization relaxation approach is presented. Finally, two set of examples are presented to compare the performance of algorithms.

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncertain parameters via adaptive control. For synchronization, we use less controllers than the dimension of the proposed system. Also, we prove that the error system is asymptotically stable by using a Lyapunov function. Numerical simulations are computed to check the analytical expressions.

In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It is shown that the proposed technique is of first order accurate and the error constant is independent of the perturbation parameter. Several problems are solved and numerical results are presented to support the theoretical error bounds established.

Steady hydromagnetic Couette flow of class-II of a viscous, incompressible and electrically conducting fluid through a porous medium in a rotating system taking Hall current into account is investigated. Heat transfer characteristics of the fluid flow are considered taking viscous and Joule dissipations into account. It is noticed that there exists flow separation at the moving plate in the secondary flow direction on increasing either rotation parameter K2 when Hall current parameter m=0.5 or m when K2=7. Also there exists flow separation at the moving plate in the secondary flow direction on increasing either magnetic parameter M2 for every value of porosity parameter K1 or K1 when M2=15.

The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are reported to demonstrate the applicably and efficiency of the propounded technique.

A common method to determine the order of minimal realization of a continuous linear time invariant descriptor system is to decompose it into slow and fast subsystems using the Weierstrass canonical form. The Weierstrass decomposition should be avoided because it is generally an ill-conditioned problem that requires many complex calculations especially for high-dimensional systems. The present study finds the order of minimal realization of a continuous linear time invariant descriptor system without use of the Weierstrass canonical form.