Analysis of finite element two-grid algorithms for two-dimensional nonlinear Schrödinger equation with wave operator

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113647 ◽

2021 ◽

pp. 113647

Author(s):

Hanzhang Hu ◽

Yanping Chen

Keyword(s):

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

Grid Algorithms

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Two-grid method for two-dimensional nonlinear Schrödinger equation by finite element method

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22193 ◽

2017 ◽

Vol 34 (2) ◽

pp. 385-400 ◽

Author(s):

Hanzhang Hu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Grid Method ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

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A linearized energy–conservative finite element method for the nonlinear Schrödinger equation with wave operator

Applied Numerical Mathematics ◽

10.1016/j.apnum.2019.02.005 ◽

2019 ◽

Vol 140 ◽

pp. 183-198 ◽

Author(s):

Wentao Cai ◽

Dongdong He ◽

Kejia Pan

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

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Numerical solution of two-dimensional nonlinear Schrödinger equation using a new two-grid finite element method

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2019.06.049 ◽

2020 ◽

Vol 364 ◽

pp. 112333 ◽

Author(s):

Hanzhang Hu ◽

Yanping Chen

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Schrödinger Equation ◽

Numerical Solution ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

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A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator

Applied Mathematics and Computation ◽

10.1016/j.amc.2021.126234 ◽

2021 ◽

Vol 404 ◽

pp. 126234

Author(s):

Yuna Yang ◽

Hongwei Li ◽

Xu Guo

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Conservative Scheme ◽

Nonlinear Schrödinger

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A conservative difference scheme for two-dimensional nonlinear Schrödinger equation with wave operator

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22033 ◽

2015 ◽

Vol 32 (3) ◽

pp. 862-876 ◽

Author(s):

Hanzhang Hu ◽

Yanping Chen

Keyword(s):

Schrödinger Equation ◽

Difference Scheme ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger ◽

Conservative Difference Scheme ◽

Conservative Difference

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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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Stability of one and two-dimensional spatial solitons in a cubic-quintic-septimal nonlinear Schrödinger equation with fourth-order diffraction and PT-symmetric potentials

Wave Motion ◽

10.1016/j.wavemoti.2021.102810 ◽

2021 ◽

pp. 102810

Author(s):

Boubakary Abdou ◽

Fabien II Ndzana ◽

Latchio Tiofack Gaston ◽

Alidou Mohamadou

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Spatial Solitons ◽

Nonlinear Schrödinger ◽

Order Diffraction

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Simple multiple explode–decay mode solutions of a two‐dimensional nonlinear Schrödinger equation

Journal of Mathematical Physics ◽

10.1063/1.525361 ◽

1982 ◽

Vol 23 (3) ◽

pp. 417-420 ◽

Author(s):

Akira Nakamura

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger

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Exact solutions of a two-dimensional nonlinear Schrödinger equation

Applied Mathematics Letters ◽

10.1016/j.aml.2011.09.030 ◽

2012 ◽

Vol 25 (4) ◽

pp. 687-691 ◽

Author(s):

Aly R. Seadawy

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Two Dimensional ◽

Nonlinear Schrödinger

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