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

Abstract 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.

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