An efficient spectral‐Galerkin method based on a dimension reduction scheme for eigenvalue problems of Schrödinger equations

Jun Zhang; Fubiao Lin; JinRong Wang

doi:10.1002/mma.5500

An efficient spectral‐Galerkin method based on a dimension reduction scheme for eigenvalue problems of Schrödinger equations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5500 ◽

2019 ◽

Vol 42 (6) ◽

pp. 2069-2082

Author(s):

Jun Zhang ◽

Fubiao Lin ◽

JinRong Wang

Keyword(s):

Galerkin Method ◽

Dimension Reduction ◽

Eigenvalue Problems ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Reduction Scheme ◽

Spectral Galerkin Method

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A conservative spectral Galerkin method for the coupled nonlinear space-fractional Schrödinger equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2018.1563687 ◽

2019 ◽

Vol 96 (12) ◽

pp. 2387-2410 ◽

Cited By ~ 2

Author(s):

Ying Wang ◽

Liquan Mei

Keyword(s):

Galerkin Method ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Fractional Schrödinger Equations ◽

Spectral Galerkin Method

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Efficient Spectral and Spectral Element Methods for Eigenvalue Problems of Schrödinger Equations with an Inverse Square Potential

SIAM Journal on Scientific Computing ◽

10.1137/16m1069596 ◽

2017 ◽

Vol 39 (1) ◽

pp. A114-A140 ◽

Cited By ~ 7

Author(s):

Huiyuan Li ◽

Zhimin Zhang

Keyword(s):

Eigenvalue Problems ◽

Spectral Element ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Spectral Element Methods

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Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Schrödinger Equations

Journal of Scientific Computing ◽

10.1007/s10915-017-0362-6 ◽

2017 ◽

Vol 73 (2-3) ◽

pp. 1290-1315 ◽

Cited By ~ 6

Author(s):

Lingling Zhou ◽

Yan Xu ◽

Zhimin Zhang ◽

Waixiang Cao

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

One Dimensional ◽

Local Discontinuous Galerkin

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Error estimates of Crank–Nicolson Galerkin method for the time-dependent Maxwell–Schrödinger equations under the Lorentz gauge

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drx060 ◽

2017 ◽

Vol 38 (4) ◽

pp. 2074-2104 ◽

Cited By ~ 1

Author(s):

Chupeng Ma ◽

Liqun Cao ◽

Yanping Lin

Keyword(s):

Galerkin Method ◽

Error Estimates ◽

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Lorentz Gauge ◽

Crank Nicolson

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A Conservative Discontinuous Galerkin Method for Nonlinear Electromagnetic Schrödinger Equations

SIAM Journal on Scientific Computing ◽

10.1137/19m124229x ◽

2019 ◽

Vol 41 (6) ◽

pp. B1389-B1411 ◽

Cited By ~ 1

Author(s):

Nianyu Yi ◽

Yunqing Huang ◽

Hailiang Liu

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equations ◽

Schrödinger Equations

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Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method

Chinese Physics B ◽

10.1088/1674-1056/21/3/030202 ◽

2012 ◽

Vol 21 (3) ◽

pp. 030202 ◽

Cited By ~ 17

Author(s):

Rong-Pei Zhang ◽

Xi-Jun Yu ◽

Tao Feng

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

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A Local Discontinuous Galerkin Method with Generalized Alternating Fluxes for 2D Nonlinear Schrödinger Equations

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-020-00100-7 ◽

2021 ◽

Author(s):

Hongjuan Zhang ◽

Boying Wu ◽

Xiong Meng

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Local Discontinuous Galerkin ◽

Nonlinear Schrodinger Equations

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An Adaptive Multiresolution Ultra-weak Discontinuous Galerkin Method for Nonlinear Schrödinger Equations

Communications on Applied Mathematics and Computation ◽

10.1007/s42967-020-00096-0 ◽

2021 ◽

Author(s):

Zhanjing Tao ◽

Juntao Huang ◽

Yuan Liu ◽

Wei Guo ◽

Yingda Cheng

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2020.1822994 ◽

2020 ◽

pp. 1-18 ◽

Cited By ~ 3

Author(s):

Mahmoud A. Zaky ◽

Ahmed S. Hendy

Keyword(s):

Galerkin Method ◽

Convergence Analysis ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Time Space ◽

Fractional Schrödinger Equations ◽

Continuous Galerkin

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Efficient Spectral-Galerkin Method for eigenvalue problems

Proceedings of the 3rd International Conference on Computer Science and Service System ◽

10.2991/csss-14.2014.23 ◽

2014 ◽

Author(s):

Jun Zhang ◽

Xinyue Fan

Keyword(s):

Galerkin Method ◽

Eigenvalue Problems ◽

Spectral Galerkin Method

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