@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} }