Volume-preserving exponential integrators and their applications

Wang, Bin; Wu, Xinyuan

doi:10.1016/j.jcp.2019.07.026

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Cited by 6 publications

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“…For other structure-preserving exponential integrators, readers are referred to Refs. [6,25,26,34]. However, to our best knowledge, there has been no reference considering structure-preserving exponential schemes for the NLS eqaution, which can inherit the properties of both mass and energy.…”

Section: Introductionmentioning

confidence: 99%

Mass- and energy-preserving exponential Runge-Kutta methods for the nonlinear Schrödinger equation

Cui¹,

Xu²,

Wang³

et al. 2020

Preprint

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In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods is developed for the nonlinear Schrödinger equation by combing the scalar auxiliary variable approach and the exponential Runge-Kutta method. By introducing an auxiliary variable, we first transform the original model into an equivalent system which admits both mass and modified energy. Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of massand energy-conserving time-discrete schemes. Numerical experiments are addressed to demonstrate the accuracy and effectiveness of the newly proposed schemes.

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Section: Introductionmentioning

confidence: 99%