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

Blow-up of the solution of a nonlinear Schrödinger equation system with periodic boundary conditions

We consider a system of nonlinear Schrödinger equations with periodic boundary conditions of the formi ∂uj/∂t + D2uj = −fj (u, ū),    t ≥ 0,  x ∈ (−2,2),uj (0, x) = uj0(x),    x ∈ (−2,2),Dkuj (t, −2) = Dkuj (t, 2),     t ≥ 0,   k = 0, 1,where D = ∂/∂x,  j = 1,..., m,  fj (u, ū) = ∂g(u, ū)/∂ū, and ∂g/∂uj = –f j for some homogenous function g(u, ū) such that g(λu, λū) = λ6g(u, ū). We obtain sufficient conditions for blow-up of solutions of this system in C1([0,t0);H2(−2,2))

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

The convergence and stability of splitting finite difference schemes for nonlinear evolutionary type equations

A splitting finite difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary type equation is considered. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional equations. The convergence and stability of the scheme in L2 and C norms are proved

VU studijų proceso finansų valdymo kompiuterinis modeliavimas

In this work a computer simulation of Vilnius University financial management is completed. The purpose of the simulation is to calculate optimal distribution of monetary reserves for each VU faculty. In addition, the conclusion is made, which budget is oriented to quality of studies and which has social aspect.Santraukos nėra

Procjena utjecaja okolišnih uvjeta na lijepljene drvne elemente u graditeljstvu

The research investigated the impact of environmental factors (temperature and humidity) on pine glulam, oak glulam, and laminated veneer lumber (LVL) elements, all of which can be used in building structures. Elements underwent freezing, heating, drying, and wetting processes in different modes, thereby simulating different environmental conditions that could be encountered during the service period of the materials. Their mechanical properties (modulus of elasticity - MOE and coefficient of damping) were recorded at each stage. It was determined that, in the case of dry construction elements (where a moisture content was between 7.0 and 14.0 %), the MOE increases by a few percentage points with decreasing temperature and humidity levels, and decreases with increasing temperature and humidity levels. The coefficient of damping varied by 20 % - in most cases, when the modulus of elasticity increased, this decreased, and vice versa. Under extreme environmental changes (with the elements being soaked, frozen at -25 °C, and dried at 40 °C), the MOE of the glued timber decreased by 16 % when this parameter of LVL decreased by about 10 %. Alterations in viscous properties produced similar results (the coefficient of damping increased by 50 % for the glued timber and by 66 % for the LVL). This is explained by the partial destruction of the element structure, the occurrence of cracks, and the decreased anisotropy of the LVL structure.U radu je istraživan utjecaj okolišnih čimbenika (temperature i vlage) na elemente lameliranih nosača izrađenih od borovine i hrastovine te na elemente lamelirane furnirske građe (LVL), koji se često rabe u graditeljstvu. Elementi su bili na različite načine podvrgnuti smrzavanju, zagrijavanju, sušenju i vlaženju kako bi se simulirali različiti okolišni uvjeti koji bi se mogli pojaviti tijekom uporabe tih materijala. U svakoj su fazi ispitivanja bilježena mehanička svojstva promatranih drvnih elemenata (modul elastičnosti – MOE i koeficijent prigušenja). Utvrđeno je da se u suhih građevinskih elemenata (sadržaj vode između 7,0 i 14,0 %) s padom temperature i vlage MOE povećava za nekoliko postotnih bodova, a smanjuje se s porastom temperature i vlage. Koeficijent prigušenja u većini je ispitivanja varirao za 20 %: kako se modul elastičnosti povećavao, koeficijent prigušenja se smanjivao, i obrnuto. Pri ekstremnim promjenama okolišnih uvjeta (potapanjem elemenata, smrzavanjem na –25 °C i sušenjem na 40 °C) MOE lameliranih nosača se smanjio za 16 %, a LVL-a za oko 10 %. Glede promjena viskoelastičnih svojstava, zabilježeni su slični rezultati (koeficijent prigušenja lameliranih nosača povećao se za 50 %, a LVL-a za 66 %). To se objašnjava djelomičnom razgradnjom strukture drvnih elemenata, pojavom pukotina i smanjenom anizotropijom strukture LVL-a

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