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Title: Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations

In this paper, we study 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. Finally, extensive numerical examples are provided to illustrate the accuracy, efficiency and reliability of the proposed methods.
 [1] ;  [1] ;  [2]
  1. Middle Tennessee State Univ., Murfreesboro, TN (United States). Dept. of Mathematical Sciences. Center for Computational Science
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division; Univ. of Tennessee, Knoxville, TN (United States). Dept. of Mathematics
Publication Date:
OSTI Identifier:
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Volume: 17; Journal Issue: 02; Journal ID: ISSN 1815-2406
Global Science Press
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Contributing Orgs:
Middle Tennessee State Univ., Murfreesboro, TN (United States)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; exponential time differencing; local discontinuous Galerkin; nonlinear Schrödinger equation; energy conserving; error estimate