@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.060414.190914a},
url = {http://global-sci.org/intro/article_detail/cicp/10967.html}
}