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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

DOI: 10.4208/cicp.060414.190914a

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 = {X. Liang, A. Q. M. Khaliq and Y. Xing}, 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 AU - X. Liang, A. Q. M. Khaliq & Y. Xing 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 and Y. Xing. (2018). 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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