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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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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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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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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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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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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Local absorbing boundary conditions for two‐dimensional nonlinear Schrödinger equation with wave operator on unbounded domain

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.7703 ◽

2021 ◽

Author(s):

Hongwei Li

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Nonlinear Schrödinger Equation ◽

Unbounded Domain ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Absorbing Boundary Conditions ◽

Two Dimensional ◽

Absorbing Boundary

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Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method

Communications in Theoretical Physics ◽

10.1088/1572-9494/ab6185 ◽

2020 ◽

Vol 72 (2) ◽

pp. 025001

Author(s):

Bin Cheng ◽

Ya-Ming Chen ◽

Chuan-Fu Xu ◽

Da-Li Li ◽

Xiao-Gang Deng

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Difference Method ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Dirac Delta ◽

Delta Potential ◽

Dirac Delta Potential

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A Fast Conservative Scheme for the Space Fractional Nonlinear Schrödinger Equation with Wave Operator

Journal of Mathematical Study ◽

10.4208/jms.v54n4.21.06 ◽

2021 ◽

Vol 54 (4) ◽

pp. 407-426

Author(s):

MustafaAlmushaira & FeiLiu

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Conservative Scheme ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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A new conservative fourth-order accurate difference scheme for the nonlinear Schrödinger equation with wave operator

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.11.005 ◽

2021 ◽

Author(s):

Labidi Samira ◽

Khaled Omrani

Keyword(s):

Schrödinger Equation ◽

Difference Scheme ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger

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