Stability and convergence analysis of artificial boundary conditions for the Schrödinger equation on a rectangular domain

Stability And Convergence Analysis

The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions

Journal of Computational Physics ◽

10.1016/j.jcp.2005.09.011 ◽

2006 ◽

Vol 214 (1) ◽

pp. 209-223 ◽

Cited By ~ 27

Author(s):

Zhi-zhong Sun ◽

Xiaonan Wu

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Difference Scheme ◽

Schrodinger Equation ◽

Stability And Convergence ◽

Infinite Domain ◽

Artificial Boundary ◽

The Stability

The stability and convergence of an explicit difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions

Journal of Computational Physics ◽

10.1016/j.jcp.2006.07.001 ◽

2006 ◽

Vol 219 (2) ◽

pp. 879-898 ◽

Cited By ~ 5

Author(s):

Zhi-zhong Sun

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Difference Scheme ◽

Schrodinger Equation ◽

Stability And Convergence ◽

Infinite Domain ◽

Artificial Boundary ◽

Explicit Difference Scheme ◽

The Stability

Construction of adaptive artificial boundary conditions using the invariant ratios for Schrödinger equation

Proceedings of IEEE East-West Design & Test Symposium (EWDTS 2014) ◽

10.1109/ewdts.2014.7027098 ◽

2014 ◽

Author(s):

Vyacheslav A. Trofimov ◽

Evgeny M. Trykin

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Artificial Boundary ◽

Exact artificial boundary conditions for the Schrödinger equation in $R ^2$

Communications in Mathematical Sciences ◽

10.4310/cms.2004.v2.n1.a5 ◽

2004 ◽

Vol 2 (1) ◽

pp. 79-94 ◽

Cited By ~ 29

Author(s):

Houde Han ◽

Zhongyi Huang

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Artificial Boundary ◽

Adaptive Artificial Boundary Conditions for 2D Schrödinger Equation

Lecture Notes in Computer Science - Numerical Analysis and Its Applications ◽

10.1007/978-3-642-41515-9_58 ◽

2013 ◽

pp. 509-516 ◽

Author(s):

Vyacheslav A. Trofimov ◽

Anton D. Denisov

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Artificial Boundary ◽

Frozen Gaussian Approximation-Based Artificial Boundary Conditions for One-Dimensional Nonlinear Schrödinger Equation in the Semiclassical Regime

Journal of Scientific Computing ◽

10.1007/s10915-017-0606-5 ◽

2017 ◽

Vol 75 (3) ◽

pp. 1701-1720 ◽

Cited By ~ 3

Author(s):

Ricardo Delgadillo ◽

Xu Yang ◽

Jiwei Zhang

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Gaussian Approximation ◽

Nonlinear Schrodinger Equation ◽

Artificial Boundary ◽

One Dimensional ◽

Semiclassical Regime

Numerical Algorithms for Schrödinger Equation with Artificial Boundary Conditions

Numerical Functional Analysis and Optimization ◽

10.1080/01630560903393097 ◽

2009 ◽

Vol 30 (9-10) ◽

pp. 903-923 ◽

Cited By ~ 10

Author(s):

R. Čiegis ◽

Inga Laukaitytė ◽

Mindaugas Radziunas

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Numerical Algorithms ◽

Artificial Boundary ◽

Adaptive artificial boundary conditions for Schrödinger equation taking into account the first order dispersion of laser pulse and diffraction of laser beam

Proceedings of IEEE East-West Design & Test Symposium (EWDTS 2014) ◽

10.1109/ewdts.2014.7027039 ◽

2014 ◽

Author(s):

Vyacheslav A. Trofimov ◽

Anton D. Denisov

Keyword(s):

Laser Pulse ◽

Schrödinger Equation ◽

Laser Beam ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Artificial Boundary ◽

First Order ◽

Order Dispersion

Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110575 ◽

2021 ◽

pp. 110575

Author(s):

Songsong Ji ◽

Gang Pang ◽

Xavier Antoine ◽

Jiwei Zhang

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Artificial Boundary ◽

One Dimensional ◽

Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions

PLoS ONE ◽

10.1371/journal.pone.0206235 ◽

2018 ◽

Vol 13 (10) ◽

pp. e0206235 ◽

Author(s):

Vyacheslav A. Trofimov ◽

Evgeny M. Trykin

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Difference Schemes ◽

Finite Difference Schemes ◽

Artificial Boundary ◽

Rosenbrock Method ◽

Implicit Finite Difference