Fourth Order Exponential Time Differencing Method with Local Discontinuous Galerkin Approximation for Coupled Nonlinear Schrödinger Equations. (23rd January 2015)

• Record Type: Journal Article
• Authors: Liang, X.; Khaliq, A. Q. M.; Xing, Y.
• Is Part Of: Communications in computational physics. Volume 17:Number 2(2015:Feb.)
• Page Start: 510
• Page End: 541
• Publication Date: 2015-01-23
• Subjects: 65M20, -- 65M60, -- 65Z05; Exponential time differencing, -- local discontinuous Galerkin, -- nonlinear Schrödinger equation, -- energy conserving, -- error estimate; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.060414.190914a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.