Unconditional optimal error estimates for BDF2-FEM for a nonlinear Schrödinger equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2017.09.010 ◽

2018 ◽

Vol 331 ◽

pp. 23-41 ◽

Author(s):

Wentao Cai ◽

Jian Li ◽

Zhangxin Chen

Keyword(s):

Schrödinger Equation ◽

Error Estimates ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Optimal Error Estimates ◽

Optimal Error ◽

Nonlinear Schrödinger

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Uniform and Optimal Error Estimates of an Exponential Wave Integrator Sine Pseudospectral Method for the Nonlinear Schrödinger Equation with Wave Operator

SIAM Journal on Numerical Analysis ◽

10.1137/120866890 ◽

2014 ◽

Vol 52 (3) ◽

pp. 1103-1127 ◽

Author(s):

Weizhu Bao ◽

Yongyong Cai

Keyword(s):

Schrödinger Equation ◽

Error Estimates ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Pseudospectral Method ◽

Nonlinear Schrodinger Equation ◽

Optimal Error Estimates ◽

Optimal Error ◽

Exponential Wave Integrator

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Unconditional convergence and optimal error estimates of the Euler semi-implicit scheme for a generalized nonlinear Schrödinger equation

Advances in Computational Mathematics ◽

10.1007/s10444-016-9463-2 ◽

2016 ◽

Vol 42 (6) ◽

pp. 1311-1330 ◽

Author(s):

Wentao Cai ◽

Jian Li ◽

Zhangxin Chen

Keyword(s):

Schrödinger Equation ◽

Error Estimates ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Implicit Scheme ◽

Unconditional Convergence ◽

Optimal Error Estimates ◽

Optimal Error ◽

Generalized Nonlinear Schrödinger Equation

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Optimal error estimate of a compact scheme for nonlinear Schrödinger equation

Applied Numerical Mathematics ◽

10.1016/j.apnum.2017.05.004 ◽

2017 ◽

Vol 120 ◽

pp. 68-81 ◽

Author(s):

Jialin Hong ◽

Lihai Ji ◽

Linghua Kong ◽

Tingchun Wang

Keyword(s):

Schrödinger Equation ◽

Error Estimate ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Compact Scheme ◽

Optimal Error Estimate ◽

Optimal Error ◽

Nonlinear Schrödinger

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Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2016.05.014 ◽

2016 ◽

Vol 442 (2) ◽

pp. 740-760 ◽

Author(s):

Johannes Eilinghoff ◽

Roland Schnaubelt ◽

Katharina Schratz

Keyword(s):

Schrödinger Equation ◽

Error Estimates ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Splitting Schemes ◽

Nonlinear Schrödinger ◽

Fractional Error

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On Optimal Order Error Estimates for the Nonlinear Schrödinger Equation

SIAM Journal on Numerical Analysis ◽

10.1137/0730018 ◽

1993 ◽

Vol 30 (2) ◽

pp. 377-400 ◽

Author(s):

Ohannes Karakashian ◽

Georgios D. Akrivis ◽

Vassilios A. Dougalis

Keyword(s):

Schrödinger Equation ◽

Error Estimates ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Optimal Order ◽

Order Error ◽

Nonlinear Schrödinger ◽

Optimal Order Error Estimates

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Error estimates of exponential wave integrator Fourier pseudospectral methods for the nonlinear Schrödinger equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.09.041 ◽

2019 ◽

Vol 343 ◽

pp. 100-113

Author(s):

Bingquan Ji ◽

Luming Zhang

Keyword(s):

Schrödinger Equation ◽

Error Estimates ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Pseudospectral Methods ◽

Nonlinear Schrödinger ◽

Exponential Wave Integrator ◽

Fourier Pseudospectral

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Nonlinear Schrödinger Equation-Based Adjoint Sensitivity Analysis

2020 International Applied Computational Electromagnetics Society Symposium (ACES) ◽

10.23919/aces49320.2020.9196096 ◽

2020 ◽

Author(s):

Mahmoud M. T. Maghrabi ◽

Mohamed H. Bakr ◽

Shiva Kumar

Keyword(s):

Sensitivity Analysis ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Adjoint Sensitivity Analysis ◽

Adjoint Sensitivity ◽

Nonlinear Schrödinger

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Higher-order nonlinear Schrödinger equation in 2D case

Tohoku Mathematical Journal ◽

10.2748/tmj/1585101619 ◽

2020 ◽

Vol 72 (1) ◽

pp. 15-37

Author(s):

Nakao Hayashi ◽

Pavel I. Naumkin

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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Some properties of small perturbations against a stationary solution of the nonlinear Schrödinger equation

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2019.109570 ◽

2020 ◽

Vol 132 ◽

pp. 109570

Author(s):

Mikhail N. Smolyakov

Keyword(s):

Schrödinger Equation ◽

Stationary Solution ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Small Perturbations ◽

Nonlinear Schrödinger

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Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.4931710 ◽

2015 ◽

Vol 25 (10) ◽

pp. 103114 ◽

Author(s):

D. J. Kedziora ◽

A. Ankiewicz ◽

A. Chowdury ◽

N. Akhmediev

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Variable Coefficients ◽

Nonlinear Schrodinger Equation ◽

Time Variable ◽

Integrable Equations ◽

Nonlinear Schrödinger

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