A New Multiscale Discontinuous Galerkin Method for the One-Dimensional Stationary Schrödinger Equation

Bo Dong; Chi-Wang Shu; Wei Wang

doi:10.1007/s10915-015-0022-7

A New Multiscale Discontinuous Galerkin Method for the One-Dimensional Stationary Schrödinger Equation

Journal of Scientific Computing ◽

10.1007/s10915-015-0022-7 ◽

2015 ◽

Vol 66 (1) ◽

pp. 321-345 ◽

Cited By ~ 5

Author(s):

Bo Dong ◽

Chi-Wang Shu ◽

Wei Wang

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Stationary Schrödinger Equation ◽

One Dimensional ◽

The One

Download Full-text

High-order multiscale discontinuous Galerkin methods for the one-dimensional stationary Schrödinger equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.112962 ◽

2020 ◽

Vol 380 ◽

pp. 112962

Author(s):

Bo Dong ◽

Wei Wang

Keyword(s):

Schrödinger Equation ◽

Discontinuous Galerkin ◽

Schrodinger Equation ◽

Discontinuous Galerkin Methods ◽

High Order ◽

Galerkin Methods ◽

Stationary Schrödinger Equation ◽

One Dimensional ◽

The One

Download Full-text

The One-Dimensional Stationary Schrödinger Equation

Basic Concepts in Computational Physics ◽

10.1007/978-3-319-02435-6_10 ◽

2013 ◽

pp. 131-146

Author(s):

Benjamin A. Stickler ◽

Ewald Schachinger

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Stationary Schrödinger Equation ◽

One Dimensional ◽

The One

Download Full-text

An adaptive high-order discontinuous Galerkin method with error control for the Hamilton–Jacobi equations. Part I: The one-dimensional steady state case

Journal of Computational Physics ◽

10.1016/j.jcp.2007.05.003 ◽

2007 ◽

Vol 226 (1) ◽

pp. 1027-1058 ◽

Cited By ~ 2

Author(s):

Yanlai Chen ◽

Bernardo Cockburn

Keyword(s):

Steady State ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Error Control ◽

High Order ◽

One Dimensional ◽

The One ◽

Jacobi Equations ◽

State Case

Download Full-text

Mean-square convergence of a symplectic local discontinuous Galerkin method applied to stochastic linear Schrödinger equation

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drw023 ◽

2016 ◽

pp. drw023

Author(s):

Chuchu Chen ◽

Jialin Hong ◽

Lihai Ji

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Mean Square ◽

Local Discontinuous Galerkin ◽

Mean Square Convergence

Download Full-text

A modified central discontinuous Galerkin method with positivity-preserving and well-balanced properties for the one-dimensional nonlinear shallow water equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.06.033 ◽

2019 ◽

Vol 345 ◽

pp. 374-387 ◽

Cited By ~ 2

Author(s):

Aimin Chen ◽

Maojun Li

Keyword(s):

Galerkin Method ◽

Shallow Water ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Shallow Water Equations ◽

Positivity Preserving ◽

One Dimensional ◽

Nonlinear Shallow Water Equations ◽

The One ◽

Central Discontinuous Galerkin

Download Full-text

A conservative local discontinuous Galerkin method for the solution of nonlinear Schrödinger equation in two dimensions

Science China Mathematics ◽

10.1007/s11425-016-9118-x ◽

2017 ◽

Vol 60 (12) ◽

pp. 2515-2530 ◽

Cited By ~ 6

Author(s):

RongPei Zhang ◽

XiJun Yu ◽

MingJun Li ◽

XiangGui Li

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Nonlinear Schrödinger Equation ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

Local Discontinuous Galerkin Method ◽

Nonlinear Schrodinger Equation ◽

Two Dimensions ◽

Local Discontinuous Galerkin

Download Full-text

A space discontinuous Galerkin method for the one-dimensional unsteady convection-diffusion equation

Water Resources Management ◽

10.1007/bf00431142 ◽

1990 ◽

Vol 4 (3) ◽

pp. 175-185 ◽

Cited By ~ 1

Author(s):

Diamandis N. Karamouzis

Keyword(s):

Diffusion Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

One Dimensional ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

The One

Download Full-text

On One Implementation of the Numerov Method for the One-Dimensional Stationary Schrödinger Equation

Physics of Particles and Nuclei Letters ◽

10.1134/s154747712102014x ◽

2021 ◽

Vol 18 (2) ◽

pp. 153-159

Author(s):

M. Purevkhuu ◽

V. I. Korobov

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Stationary Schrödinger Equation ◽

One Dimensional ◽

Numerov Method ◽

The One

Download Full-text

Optimal energy-conserving local discontinuous Galerkin method for the one-dimensional sine-Gordon equation

International Journal of Computer Mathematics ◽

10.1080/00207160.2015.1105364 ◽

2015 ◽

Vol 94 (2) ◽

pp. 316-344 ◽

Cited By ~ 7

Author(s):

Mahboub Baccouch

Keyword(s):

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Gordon Equation ◽

Local Discontinuous Galerkin Method ◽

Sine Gordon Equation ◽

One Dimensional ◽

Local Discontinuous Galerkin ◽

Energy Conserving ◽

The One

Download Full-text

An Ultra-weak Discontinuous Galerkin Method for Schrödinger Equation in One Dimension

Journal of Scientific Computing ◽

10.1007/s10915-018-0789-4 ◽

2018 ◽

Vol 78 (2) ◽

pp. 772-815 ◽

Cited By ~ 2

Author(s):

Anqi Chen ◽

Fengyan Li ◽

Yingda Cheng

Keyword(s):

Schrödinger Equation ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Schrodinger Equation ◽

One Dimension

Download Full-text