oalib

Publish in OALib Journal

ISSN: 2333-9721

APC: Only $99

Submit

Any time

2020 ( 6 )

2019 ( 33 )

2018 ( 54 )

2017 ( 45 )

Custom range...

Search Results: 1 - 10 of 19803 matches for " Alexander Zlotnik "
All listed articles are free for downloading (OA Articles)
Page 1 /19803
Display every page Item
Some remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schr?dinger equation on the half-axis
Alexander Zlotnik,Ilya Zlotnik
Mathematics , 2014,
Abstract: We consider the generalized time-dependent Schr\"odinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a simplified form explicit in space step $h$. Next, for a selected scheme of the family, we discover that the discrete convolution in time in the discrete TBC does not depend on $h$ and, moreover, it coincides with the corresponding convolution in the semi-discrete TBC rewritten similarly. This allows us to prove the bound for the difference between the kernels of the discrete convolutions in the discrete and semi-discrete TBCs (for the first time). Numerical experiments on replacing the discrete TBC convolutions by the semi-discrete one exhibit truly small absolute errors though not relative ones in general. The suitable discretization in space of the semi-discrete TBC for the higher-order Numerov scheme is also discussed.
On the rate of the volume growth for symmetric viscous heat-conducting gas flows with a free boundary
Alexander Zlotnik
Abstract and Applied Analysis , 2006, DOI: 10.1155/aaa/2006/16071
Abstract: The system of quasilinear equations for symmetric flows of aviscous heat-conducting gas with a free external boundary isconsidered. For global in time weak solutions having nonstrictlypositive density, the linear in time two-sided bounds for the gasvolume growth are established.
On the rate of the volume growth for symmetric viscous heat-conducting gas flows with a free boundary
Alexander Zlotnik
Abstract and Applied Analysis , 2006,
Abstract: The system of quasilinear equations for symmetric flows of a viscous heat-conducting gas with a free external boundary is considered. For global in time weak solutions having nonstrictly positive density, the linear in time two-sided bounds for the gas volume growth are established.
On Error Estimates of the Crank-Nicolson-Polylinear Finite Element Method with the Discrete TBC for the Generalized Schr?dinger Equation in an Unbounded Parallelepiped
Alexander Zlotnik
Mathematics , 2015,
Abstract: We deal with an initial-boundary value problem for the generalized time-dependent Schr\"odinger equation with variable coefficients in an unbounded $n$--dimensional parallelepiped ($n\geq 1$). To solve it, the Crank-Nicolson in time and the polylinear finite element in space method with the discrete transpa\-rent boundary conditions is considered. We present its stability properties and derive new error estimates $O(\tau^2+|h|^2)$ uniformly in time in $L^2$ space norm, for $n\geq 1$, and mesh $H^1$ space norm, for $1\leq n\leq 3$ (a superconvergence result), under the Sobolev-type assumptions on the initial function. Such estimates are proved for methods with the discrete TBCs for the first time.
On symmetric equilibrium of an isothermal gas with a free boundary and a body force
Alexander Zlotnik,Mikhail Maksimov
Abstract and Applied Analysis , 2006, DOI: 10.1155/aaa/2006/69347
Abstract: The equation of symmetric equilibrium of an isothermal gas with anunknown boundary in the field of a body force is considered.Conditions for solvability and insolvability of the problem aswell as for uniqueness and nonuniqueness of solutions arepresented. Examples of finite, countable, or continual sets ofsolutions are constructed including equipotential ones. Staticstability of solutions is analyzed too.
On symmetric equilibrium of an isothermal gas with a free boundary and a body force
Alexander Zlotnik,Mikhail Maksimov
Abstract and Applied Analysis , 2006,
Abstract: The equation of symmetric equilibrium of an isothermal gas with an unknown boundary in the field of a body force is considered. Conditions for solvability and insolvability of the problem as well as for uniqueness and nonuniqueness of solutions are presented. Examples of finite, countable, or continual sets of solutions are constructed including equipotential ones. Static stability of solutions is analyzed too.
On a regularization of the magnetic gas dynamics system of equations
Bernard Ducomet,Alexander Zlotnik
Physics , 2012,
Abstract: A brief derivation of a specific regularization for the magnetic gas dynamic system of equations is given in the case of general equations of gas state (in presence of a body force and a heat source). The entropy balance equation in two forms is also derived for the system. For a constant regularization parameter and under a standard condition on the heat source, we show that the entropy production rate is nonnegative.
On a family of finite-difference schemes with discrete transparent boundary conditions for a parabolic equation on the half-axis
Alexander Zlotnik,Natalya Koltsova
Mathematics , 2012,
Abstract: An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averagings both in time and space. Stability in two norms is proved by the energy method. Also discrete transparent boundary conditions are rigorously derived for schemes by applying the method of reproducing functions. Results of numerical experiments are included as well.
Stabilization for equations of one-dimensional viscous compressible heat-conducting media with nonmonotone equation of state
Bernard Ducomet,Alexander Zlotnik
Mathematics , 2002,
Abstract: We consider the Navier-Stokes system describing motions of viscous compressible heat-conducting and "self-gravitating" media. We use the state function of the form $p(\eta,\theta)=p_0(\eta)+p_1(\eta)\theta$ linear with respect to the temperature $\theta$, but we admit rather general nonmonotone functions $p_0$ and $p_1$ of $\eta$, which allows us to treat various physical models of nuclear fluids (for which $p$ and $\eta$ are the pressure and specific volume) or thermoviscoelastic solids. For an associated initial-boundary value problem with "fixed-free" boundary conditions and possibly large data, we prove a collection of estimates independent of time interval for solutions, including two-sided bounds for $\eta$, together with its asymptotic behaviour as $t\to \infty$. Namely, we establish the stabilization pointwise and in $L^q$ for $\eta$, in $L^2$ for $\theta$, and in $L^q$ for $v$ (the velocity), for any $q\in[2,\infty)$.
A Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schr?dinger equation on a semi-infinite strip
Alexander Zlotnik,Alla Romanova
Mathematics , 2013,
Abstract: We consider an initial-boundary value problem for a 2D time-dependent Schr\"odinger equation on a semi-infinite strip. For the Numerov-Crank-Nicolson finite-difference scheme with discrete transparent boundary conditions, the Strang-type splitting with respect to the potential is applied. For the resulting method, the uniqueness of a solution and the uniform in time $L^2$-stability (in particular, $L^2$-conservativeness) are proved. Due to the splitting, an effective direct algorithm using FFT in the direction perpendicular to the strip is developed to implement the splitting method for general potential. Numerical results on the tunnel effect for smooth and rectangular barriers together with the practical error analysis on refining meshes are included as well.
Page 1 /19803
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.