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DOE OSTI · 1286709

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

Liang, Xiao·Khaliq, Abdul Q. M.·Xing, Yulong
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Abstract

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.

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97 MATHEMATICS AND COMPUTINGenergy conservingerror estimateexponential time differencinglocal discontinuous Galerkinnonlinear Schrödinger equation

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Liang, Xiao, Khaliq, Abdul Q. M., Xing, Yulong. 2015-01-23. Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations. https://doi.org/10.4208/cicp.060414.190914a

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