Relaxation techniques applied after each time step to IMEX Runge-Kutta schemes ensure that fully discrete Schrödinger-Poisson systems conserve mass and satisfy energy balance equations up to rounding errors.
A Fourier collocation method for Schr¨ odinger-Poisson system with perfectly matched layer.Communications in Mathematical Sciences, 20(2):523 – 542, 2022
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Efficient High-order Mass-conserving and Energy-balancing Schemes for Schr\"odinger-Poisson Equations
Relaxation techniques applied after each time step to IMEX Runge-Kutta schemes ensure that fully discrete Schrödinger-Poisson systems conserve mass and satisfy energy balance equations up to rounding errors.