Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations (Communications in Computational Physics, 2020)
This paper studies a local discontinuous Galerkin method combined withfourth order exponential time differencing Runge-Kutta time discretization and a fourthorder conservative method for solving the nonlinear Schrödinger equations. Based ondifferent choices of numerical fluxes, we propose both energy-conserving and energy-dissipativelocal discontinuous Galerkin methods, and have proven the error estimatesfor the semi-discrete methods applied to linear Schrödinger equation. The numericalmethods are proven to be highly efficient and stable for long-range soliton computations.Extensive numerical examples are provided to illustrate the accuracy, efficiencyand reliability of the proposed methods.