scholarly journals On stability of the Crank-Nicolson scheme with approximate transparent boundary conditions for the Schrödinger equation. I

2006 ◽  
Vol 4 (4) ◽  
pp. 741-766 ◽  
Author(s):  
B. Ducomet ◽  
B. Ducomet ◽  
A. Zlotnik ◽  
A. Zlotnik
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Transparent Boundary Conditions ◽  
Nicolson Scheme ◽  
Crank Nicolson

scholarly journals ON THE ACCURACY OF SOME ABSORBING BOUNDARY CONDITIONS FOR THE SCHRODINGER EQUATION

2017 ◽  
Vol 22 (3) ◽  
pp. 408-423 ◽  
Author(s):  
Andrej Bugajev ◽  
Raimondas Čiegis ◽  
Rima Kriauzienė ◽  
Teresė Leonavičienė ◽  
Julius Žilinskas
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Rational Functions ◽  
Detailed Comparison ◽  
Absorbing Boundary Conditions ◽  
Benchmark Problems ◽  
Transparent Boundary Conditions ◽  
Absorbing Boundary ◽  
L2 Norm

A detailed analysis of absorbing boundary conditions for the linear Schrodinger equation is presented in this paper. It is focused on absorbing boundary conditions that are obtained by using rational functions to approximate the exact transparent boundary conditions. Different strategies are investigated for the optimal selection of the coefficients of these rational functions, including the Pade approximation, the L2 norm approximations of the Fourier symbol, L2 minimization of a reflection coefficient, and two error minimization techniques for the chosen benchmark problems with known exact solutions. The results of computational experiments are given and a detailed comparison of the efficiency of these techniques is presented.

Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Alexander Zlotnik ◽  
Ilya Zlotnik
Keyword(s):  
Finite Difference ◽  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Finite Difference Schemes ◽  
Transparent Boundary Conditions ◽  
Space Step ◽  
Half Axis ◽  
Generalized Time

AbstractWe consider the generalized time-dependent Schrödinger 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

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