The finite difference scheme for nonlinear Schrödinger equations on unbounded domain by artificial boundary conditions

Applied Numerical Mathematics ◽

10.1016/j.apnum.2018.02.005 ◽

2018 ◽

Vol 128 ◽

pp. 183-204 ◽

Cited By ~ 4

Author(s):

Bo Wang ◽

Dong Liang

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Unbounded Domain ◽

Finite Difference Scheme ◽

Nonlinear Schrödinger Equations ◽

Schrödinger Equations ◽

Artificial Boundary ◽

Artificial Boundary Conditions ◽

Nonlinear Schrodinger Equations

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A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions

Journal of Computational Physics ◽

10.1016/j.jcp.2011.12.028 ◽

2012 ◽

Vol 231 (7) ◽

pp. 2865-2879 ◽

Cited By ~ 62

Author(s):

Guang-hua Gao ◽

Zhi-zhong Sun ◽

Ya-nan Zhang

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Unbounded Domain ◽

Finite Difference Scheme ◽

Diffusion Equations ◽

Artificial Boundary ◽

Artificial Boundary Conditions

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Efficient semi-implicit compact finite difference scheme for nonlinear Schrödinger equations on unbounded domain

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.02.014 ◽

2020 ◽

Vol 153 ◽

pp. 319-343

Author(s):

Yunxia Hu ◽

Hongwei Li ◽

Ziwen Jiang

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Unbounded Domain ◽

Finite Difference Scheme ◽

Nonlinear Schrödinger Equations ◽

Schrödinger Equations ◽

Compact Finite Difference Scheme ◽

Compact Finite Difference ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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A linearized, decoupled, and energy-preserving compact finite difference scheme for the coupled nonlinear Schrödinger equations

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22125 ◽

2016 ◽

Vol 33 (3) ◽

pp. 840-867 ◽

Cited By ~ 11

Author(s):

Tingchun Wang

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Nonlinear Schrödinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Compact Finite Difference Scheme ◽

Compact Finite Difference ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations

Journal of Evolution Equations ◽

10.1007/s00028-020-00585-y ◽

2020 ◽

Author(s):

Younghun Hong ◽

Chulkwang Kwak ◽

Shohei Nakamura ◽

Changhun Yang

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Discrete artificial boundary conditions for nonlinear Schrödinger equations

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2007.07.007 ◽

2008 ◽

Vol 47 (11-12) ◽

pp. 1264-1283 ◽

Cited By ~ 7

Author(s):

Andrea Zisowsky ◽

Matthias Ehrhardt

Keyword(s):

Boundary Conditions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Artificial Boundary ◽

Artificial Boundary Conditions ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations

SIAM Journal on Numerical Analysis ◽

10.1137/040606983 ◽

2006 ◽

Vol 43 (6) ◽

pp. 2272-2293 ◽

Cited By ~ 51

Author(s):

Xavier Antoine ◽

Christophe Besse ◽

Stephane Descombes

Keyword(s):

Boundary Conditions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Artificial Boundary ◽

One Dimensional ◽

Artificial Boundary Conditions ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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A new high‐order accurate conservative finite difference scheme for the coupled nonlinear Schrödinger equations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7579 ◽

2021 ◽

Author(s):

Yuyu He ◽

Xiaofeng Wang ◽

Weizhong Dai ◽

Yaqing Deng

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

High Order ◽

Nonlinear Schrödinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Conservative Finite Difference Scheme

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Optimal Point-Wise Error Estimate of a Compact Finite Difference Scheme for the Coupled Nonlinear Schrödinger Equations

Journal of Computational Mathematics ◽

10.4208/jcm.1310-m4340 ◽

2014 ◽

Vol 32 (1) ◽

pp. 58-74 ◽

Cited By ~ 12

Author(s):

Tingchun Wang

Keyword(s):

Finite Difference ◽

Error Estimate ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Optimal Point ◽

Compact Finite Difference Scheme ◽

Compact Finite Difference ◽

Nonlinear Schrodinger Equations

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A second-order accurate finite difference scheme for a class of nonlocal parabolic equations with natural boundary conditions

Journal of Computational and Applied Mathematics ◽

10.1016/s0377-0427(96)00097-0 ◽

1996 ◽

Vol 76 (1-2) ◽

pp. 137-146 ◽

Cited By ~ 23

Author(s):

Zhi-Zhong Sun

Keyword(s):

Finite Difference ◽

Boundary Conditions ◽

Difference Scheme ◽

Parabolic Equations ◽

Finite Difference Scheme ◽

Second Order ◽

Natural Boundary ◽

Nonlocal Parabolic Equations ◽

Natural Boundary Conditions

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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 ◽

Cited By ~ 1

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 ◽

Artificial Boundary Conditions ◽

Rosenbrock Method ◽

Implicit Finite Difference

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