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Title: Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

Abstract

In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

Authors:
 [1];  [1];  [2]
  1. Middle Tennessee State Univ., Murfreesboro, TN (United States). Dept. of Mathematical Sciences. Center for Computational Science
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division; Univ. of Tennessee, Knoxville, TN (United States). Dept. of Mathematics
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Contributing Org.:
Middle Tennessee State Univ., Murfreesboro, TN (United States)
OSTI Identifier:
1286709
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Volume: 17; Journal Issue: 02; Journal ID: ISSN 1815-2406
Publisher:
Global Science Press
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; exponential time differencing; local discontinuous Galerkin; nonlinear Schrödinger equation; energy conserving; error estimate

Citation Formats

Liang, Xiao, Khaliq, Abdul Q. M., and Xing, Yulong. Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations. United States: N. p., 2015. Web. doi:10.4208/cicp.060414.190914a.
Liang, Xiao, Khaliq, Abdul Q. M., & Xing, Yulong. Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations. United States. doi:10.4208/cicp.060414.190914a.
Liang, Xiao, Khaliq, Abdul Q. M., and Xing, Yulong. Fri . "Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations". United States. doi:10.4208/cicp.060414.190914a. https://www.osti.gov/servlets/purl/1286709.
@article{osti_1286709,
title = {Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations},
author = {Liang, Xiao and Khaliq, Abdul Q. M. and Xing, Yulong},
abstractNote = {In this paper, we study a local discontinuous Galerkin method combined with fourth order exponential time differencing Runge-Kutta time discretization and a fourth order conservative method for solving the nonlinear Schrödinger equations. Based on different choices of numerical fluxes, we propose both energy-conserving and energy-dissipative local discontinuous Galerkin methods, and have proven the error estimates for the semi-discrete methods applied to linear Schrödinger equation. The numerical methods are proven to be highly efficient and stable for long-range soliton computations. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.},
doi = {10.4208/cicp.060414.190914a},
journal = {Communications in Computational Physics},
number = 02,
volume = 17,
place = {United States},
year = {Fri Jan 23 00:00:00 EST 2015},
month = {Fri Jan 23 00:00:00 EST 2015}
}

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Cited by: 14 works
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