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 - <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>