相关论文: Semi-spectral Chebyshev method in Quantum Mechanic…
The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes…
This work investigates two physics-based models that simulate the non-linear partial differential algebraic equations describing an electric double layer supercapacitor. In one model the linear dependence between electrolyte concentration…
Moved by the need for rigorous and reliable numerical tools for the analysis of peridynamic materials, the authors propose a model able to capture the dispersive features of nonlocal soliton-like solutions obtained by a peridynamic…
This paper presents a novel approach to rigorously solving initial value problems for semilinear parabolic partial differential equations (PDEs) using fully spectral Fourier-Chebyshev expansions. By reformulating the PDE as a system of…
We extend the notion of some energy-type expressions based on two sets, developed in the abstract potential theory. We also give the discretized version of the quantities defined, similar to Chebyshev constant. This extension allows to…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its…
In this manuscript, we investigate optimal control problems which arise in connection with manipulation of dissipative quantum dynamics. These problems motivate the study of a class of dissipative bilinear control systems. For these systems…
Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a…
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving Schr\"o{}dinger equation. In order to pass the information among grids we use the values of the fields only at the contact…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…
We present a numerical spectral method to solve systems of differential equations on an infinite interval $y\in (-\infty, \infty)$ in presence of linear differential operators of the form $Q(y) \left(\partial/\partial_y\right)^b$ (where…
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes…
With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving…
We present a new exactly solvable quantum problem for which the Schroedinger equation allows for separation of variables in oblate spheroidal coordinates. Namely, this is the quantum mechanical two Coulomb centers problem for the case of…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical…