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

Liang, Xiao; Khaliq, Abdul Q. M.; Xing, Yulong

doi:10.4208/cicp.060414.190914a

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

Journal Article · Fri Jan 23 00:00:00 EST 2015 · Communications in Computational Physics

DOI:https://doi.org/10.4208/cicp.060414.190914a· OSTI ID:1286709

Liang, Xiao ^[1]; Khaliq, Abdul Q. M. ^[1]; Xing, Yulong ^[2]

Middle Tennessee State Univ., Murfreesboro, TN (United States). Dept. of Mathematical Sciences. Center for Computational Science
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

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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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Contributing Organization:: Middle Tennessee State Univ., Murfreesboro, TN (United States)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1286709

Journal Information:: Communications in Computational Physics, Vol. 17, Issue 02; ISSN 1815-2406

Publisher:: Global Science PressCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 43 works

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An energy-preserving Crank-Nicolson Galerkin method for Hamiltonian partial differential equations: Energy-Preserving Crank-Nicolson Galerkin Method Li, Haochen; Wang, Yushun; Sheng, Qin Numerical Methods for Partial Differential Equations, Vol. 32, Issue 5 https://doi.org/10.1002/num.22062	journal	April 2016
Superconvergence of Ultra-Weak Discontinuous Galerkin Methods for the Linear Schrödinger Equation in One Dimension Chen, Anqi; Cheng, Yingda; Liu, Yong Journal of Scientific Computing, Vol. 82, Issue 1 https://doi.org/10.1007/s10915-020-01124-0	journal	January 2020
Compact and efficient conservative schemes for coupled nonlinear Schrödinger equations: Compact and Efficient Conservative Schemes for CNLS Kong, Linghua; Hong, Jialin; Ji, Lihai Numerical Methods for Partial Differential Equations, Vol. 31, Issue 6 https://doi.org/10.1002/num.21969	journal	February 2015

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

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