Initial Boundary-Value Problems for Derivative Nonlinear Schroedinger Equation. Justification of Two-Step Algorithm

We investigate two different initial boundary-value problems for derivative nonlinear Schrödinger equation. The boundary conditions are Dirichlet or generalized periodic ones. We propose a two-step algorithm for numerical solving of this problem. The method consists of Bäcklund type transformations and difference scheme. We prove the convergence and stability in C and H1 norms of Crank–Nicolson finite difference scheme for the transformed problem. There are no restrictions between space and time grid steps. For the derivative nonlinear Schrödinger equation, the proposed numerical algorithm converges and is stable in C1 norm

Finite Difference Solution Methods for a System of the Nonlinear Schrödinger Equations

This paper investigates finite difference schemes for solving a system of the nonlinear Schrödinger (NLS) equations. Several types of schemes, including explicit, implicit, Hopscotch-type and Crank-Nicholson-type are defined. Cubic spline interpolation is used for solving time-shifting part of equations. The numerical results of the different solution methods are compared using two analytical invariant properties

Application of ohe Total Aproximation Method for the Investigation of the Temperature Regime of a Polychromatic Solid-State Lamp

In this paper the application of the total approximation method for polychromatic solid-state lamp was considered. The main goal of this work was to present an investigation method for the temperature regime of n LEDs based on the investigation of the temperature regime of one LED. There were presented numerical results of the investigated problem

Front Dynamics with Delays in a Spatially Extended Bistable System: Computer Simulation

Front dynamics with delays in a spatially extended bistable system of the reaction-diffusion type is studied by the use of nonlinear partial differential equation (PDE) of the parabolic type. The response of the self-ordered front, joining two steady states of the different stability in the system, to the multi-harmonic (step-like) force is examined. The relaxation rate of the system, that characterizes the delayed response of the front to the alternating current (ac) drive, is found to be sensitive to the peculiarities (shape) of the rate function (nonlinearity) of the governing PDE. By using computer simulations of the drift motion of the ac driven bistable front (BF) we are able to show that the characteristic relaxation time of the system decreases with the increasing outer slope parameters of the rate function and is not sensitive to the inner one

Modeling of Pulse Propagation Factor Changes in Type II Second Harmonic Generation

We describe the simulations of the second harmonic generation of ultrashort laser pulses by numerically solving a system of wave propagation equations. The equations are solved by using a split-step method in twodimensional cyllindrically symmetric space and time coordinates. The diffraction part of a solution uses the Hopscotch type finite-difference scheme on a regular grid. The transport part is solved by using the cubic spline approximation. The obtained numerical results satisfactorily respect energy conservation constraints. The algorithm and program developed make it possible to optimize the process of the second harmonics generation and to identify the conditions where sufficiently high degree of the pulse compression with a relatively low degradation of their quality is achieved

FDVis: the Interactive Visualization and Steering Environment for the Computational Processes Using the Finite-Difference Method

In this paper a specialized software environment for visualization and steering of finite-difference computations is presented. The user requirements are identified and the architecture of the environment is summarized. The advantages of such a specialized system over some available universal visualization systems are discussed and conclusions and future research issues are given

Modelling of a microreactor on heterogeneous surface and an influence of microreactor geometry

A model of an action of the amperometric biosensors based on carbon paste electrodes encrusted with single microreactor is analyzed. The model is based on non stationary diffusion equations containing non-linear term related to the enzymatic reaction. The biosensors current, which is a function of the concentration gradient of the reaction product on the electrodes, is used for analyzing of dynamics of the reaction. An influence of a size of microreactor, a geometrical form of microreactor and a position of microreactor on the biosensors action is investigated

Modelling of wood drying and an influence of lumber geometry on drying dynamics

Modelling of wood drying is analyzed. Wood drying involves moisture transfer from the interior of the wood to the surface, then from the wood surface to the surrounding air. These processes can be characterized by the internal and surface moisture transfer coefficients. A model of the two-dimensional moisture transfer is suggested to determine these coefficients in contrast to the one-dimensional model which was proposed in [12]. The model is based on a diffusion equation with a variable diffusion coefficient. The insufficiency of the one-dimensional model is considered. The influence of the geometry of a lumber on determination of the surface emission and diffusion coefficients and on the dynamics of drying is investigated

On Duffing equation with random perturbations

We consider a family of particles with different initial states and/or velocities whose dynamics is described by a modified Duffing equation with random perturbations. Sufficient conditions ensuring almost identical sample paths of the particles after a long time are given