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.
SAV Galerkin-Legendre spectral method for the nonlinear Schr¨ odinger-Poisson equations.Electronic Research Archive, 30(3):943–960, 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.