A novel numerical approach to solving Schr odinger's equation as applied to quantum well heterostructures is described. The quantum mechanical energy subbands, wave functions and charge density are calculated based on a two-directional fourthorder Runge-Kutta (RK4) algorithm. The algorithm is applied to well-de ned quantum well structures. Results are compared with analytic solutions to ensure...

This report is devoted to the study and to the comparison of methods for estimation of the local error and for adaptive step-size control when solving the generalised nonlinear Schrodinger equation (GNLSE) in optics by the Interaction Picture (IP) method or by the Symmetric Split-Step (S3F) method. Namely, we propose and study the use of an embedded Runge-Kutta method to solve the nonlinear pro...

In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is base...

This work deals with the modeling of the material flow in Friction Stir Welding (FSW) processes using particle tracing method. For the computation of particle trajectories, three accurate and computationally efficient integration methods are implemented within a FE model for FSW process: the Backward Euler with Substepping (BES), the 4-th order Runge-Kutta (RK4) and the Back and Forth Error Com...

Dengue is a complex disease because of the link it forms between humans, mosquitoes, and several virus serotypes, including efficient strategies for vector survival strategies. For this reason, the understanding of various factors that influence the recurrence of Dengue has been an inescapable fight for policy makers and scientists alike. In this paper, the susceptible-infected-recovered (SIR) ...

0096-3003/$ see front matter 2012 Elsevier Inc doi:10.1016/j.amc.2012.01.006 ⇑ Corresponding author. E-mail address: [email protected] (R. Jiwar In this article, we proposed a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of two dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary condition. The PDQM redu...

A deterministic mathematical model for the transmission dynamics of Influenza is studied. Although the equilibria of the model could not be expressed in closed form, their existence and threshold conditions for their stability are theoretically investigated. It is shown that the diseasefree equilibrium is locally–asymptotically stable if the basic reproductive number R0 < 1 (thus, Influenza can...

In this article, we proposed a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of one dimensional hyperbolic telegraph equation. The hyperbolic partial differential equations model the vibrations of structures (e.g., buildings, beams, and machines) and they are the basis for fundamental equations of atomic physics. The PDQM reduced t...

Childhood vaccination programs have had a dramatic impact on child morbidity and mortality. Protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators. A SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is presented in this paper. We introduce fractional-order into the presented mode...