Two novel classes of linear high-order structure-preserving schemes for the generalized nonlinear Schrodinger equation

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.