Volume 17, Issue 2
Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations

X. Liang, A. Q. M. Khaliq & Y. Xing

Commun. Comput. Phys., 17 (2015), pp. 510-541.

Published online: 2018-04

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  • Abstract

This paper studies 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. Extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

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@Article{CiCP-17-510, author = {}, title = {Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {2}, pages = {510--541}, abstract = {

This paper studies 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. Extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.060414.190914a}, url = {http://global-sci.org/intro/article_detail/cicp/10967.html} }
TY - JOUR T1 - Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations JO - Communications in Computational Physics VL - 2 SP - 510 EP - 541 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.060414.190914a UR - https://global-sci.org/intro/article_detail/cicp/10967.html KW - AB -

This paper studies 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. Extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.

X. Liang, A. Q. M. Khaliq & Y. Xing. (2020). Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations. Communications in Computational Physics. 17 (2). 510-541. doi:10.4208/cicp.060414.190914a
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