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.
Convergence of a Strang splitting finite element discretization for the Schr¨ odinger–Poisson equation.ESAIM: Mathematical Modelling and Numerical Analysis, 51(4):1245–1278, 2017
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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.