Uniform Error Estimates of Finite Difference Methods for the Nonlinear Schrödinger Equation with Wave Operator

SIAM Journal on Numerical Analysis ◽

10.1137/110830800 ◽

2012 ◽

Vol 50 (2) ◽

pp. 492-521 ◽

Author(s):

Weizhu Bao ◽

Yongyong Cai

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Error Estimates ◽

Wave Operator ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Nonlinear Schrodinger Equation ◽

Uniform Error ◽

Difference Methods ◽

Uniform Error Estimates

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Uniform point-wise error estimates of semi-implicit compact finite difference methods for the nonlinear Schrödinger equation perturbed by wave operator

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2014.08.026 ◽

2015 ◽

Vol 422 (1) ◽

pp. 286-308 ◽

Author(s):

Tingchun Wang

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Error Estimates ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Nonlinear Schrodinger Equation ◽

Compact Finite Difference ◽

Difference Methods

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Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods

10.1063/1.4995862 ◽

2017 ◽

Author(s):

Azhar Ahmad ◽

Amirah Azmi ◽

Ahmad Abd. Majid ◽

Nur Nadiah Abd Hamid

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Spline Interpolation ◽

Finite Difference Methods ◽

Nonlinear Schrodinger Equation ◽

B Spline ◽

Nonlinear Schrödinger ◽

Difference Methods

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Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods on dual solitons

10.1063/1.4980908 ◽

2017 ◽

Author(s):

Azhar Ahmad ◽

Amirah Azmi ◽

Ahmad Abd. Majid ◽

Nur Nadiah Abd Hamid

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Spline Interpolation ◽

Finite Difference Methods ◽

Nonlinear Schrodinger Equation ◽

B Spline ◽

Nonlinear Schrödinger ◽

Difference Methods

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A compact finite difference scheme for the nonlinear Schrödinger equation with wave operator

Applied Mathematics and Computation ◽

10.1016/j.amc.2012.09.051 ◽

2012 ◽

Vol 219 (6) ◽

pp. 3187-3197 ◽

Author(s):

Xin Li ◽

Luming Zhang ◽

Shanshan Wang

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Difference Scheme ◽

Nonlinear Schrödinger Equation ◽

Finite Difference Scheme ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Compact Finite Difference Scheme ◽

Compact Finite Difference

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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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Absorption of waves by complex surface layers in the solution of the Schrödinger equation by finite difference methods

Computer Physics Communications ◽

10.1016/0010-4655(83)90091-7 ◽

1983 ◽

Vol 30 (3) ◽

pp. 243-247 ◽

Author(s):

Norbert Grün ◽

Werner Scheid

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Complex Surface ◽

Surface Layers ◽

Difference Methods

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On finite difference methods for the solution of the Schrödinger equation

Computers & Chemistry ◽

10.1016/s0097-8485(99)00023-6 ◽

1999 ◽

Vol 23 (6) ◽

pp. 513-554 ◽

Author(s):

T.E. Simos ◽

P.S. Williams

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Difference Methods

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High Order Stable Finite Difference Methods for the Schrödinger Equation

Journal of Scientific Computing ◽

10.1007/s10915-012-9628-1 ◽

2012 ◽

Vol 55 (1) ◽

pp. 173-199 ◽

Author(s):

A. Nissen ◽

G. Kreiss ◽

M. Gerritsen

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Finite Difference Methods ◽

Difference Methods

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Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

Numerical Algorithms ◽

10.1007/s11075-021-01159-w ◽

2021 ◽

Author(s):

Ying Ma ◽

Jia Yin

Keyword(s):

Dirac Equation ◽

Finite Difference ◽

Error Estimates ◽

Finite Difference Methods ◽

Difference Methods

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Linear High-Order Energy-Preserving Schemes for the Nonlinear Schrödinger Equation with Wave Operator Using the Scalar Auxiliary Variable Approach

Journal of Scientific Computing ◽

10.1007/s10915-021-01533-9 ◽

2021 ◽

Vol 88 (1) ◽

Author(s):

Xin Li ◽

Yuezheng Gong ◽

Luming Zhang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Auxiliary Variable ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Order Energy ◽

Variable Approach

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