Journal
APPLIED MATHEMATICS LETTERS
Volume 104, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2020.106273
Keywords
Generalized nonlinear Schrodinger equation; Linear high-order schemes; Mass-preserving; Runge-Kutta methods; Prediction-correction
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Funding
- University Natural Science Research Key Project of Anhui Province, PR China [KJ2018A0523]
- Foundation of Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems [202002]
- Nature Science Foundation of Jiangsu Province [BK20180413]
- National Nature Science Foundation of China [11801269]
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In this letter, we present two novel classes of linear high-order mass-preserving schemes for the generalized nonlinear Schrodinger equation. The original model is first equivalently transformed into a pair of real-valued equations, which are then linearized by the extrapolation technique. We employ the symplectic Runge-Kutta method for the resulting linearized model to derive a class of linear mass-conserving schemes. To improve the accuracy of the schemes, a prediction-correction strategy is applied to develop a class of prediction-correction schemes. The proposed methods are shown to be linear, mass-preserving and may reach high order. To match the high precision of temporal discretization, the Fourier pseudo-spectral method is utilized for spatial discretization. Numerical results are shown to verify the accuracy and conservation property of the proposed schemes. (C) 2020 Elsevier Ltd. All rights reserved.
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