Efficient High-order Mass-conserving and Energy-balancing Schemes for Schrödinger-Poisson Equations

Manvendra Pratap Rajvanshi; David I. Ketcheson

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arXiv · 2604.05940

Efficient High-order Mass-conserving and Energy-balancing Schemes for Schrödinger-Poisson Equations

Manvendra Pratap Rajvanshi·David I. Ketcheson

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Abstract

We study relaxation-based approaches for conserving mass and energy in the numerical solution of Schrödinger-Poisson (SP) type systems. Relaxation-based methods offer a general approach that can be applied as post-time step processing to achieve conservation with any time-stepping scheme. Here we study two types of relaxation techniques applied to implicit-explicit Runge-Kutta schemes, with Fourier collocation in space. We also study SP equations with time-varying coefficients (which appear naturally in cosmology) where energy is not conserved but satisfies a balance equation. We show that the fully-discrete system conserves both mass and energy (or satisfies the balance equation in case of time-varying coefficients), up to rounding errors. The effectiveness of these methods is demonstrated via numerical examples, including a three-dimensional cosmological simulation.

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Manvendra Pratap Rajvanshi, David I. Ketcheson. 2026-04-07. Efficient High-order Mass-conserving and Energy-balancing Schemes for Schrödinger-Poisson Equations. https://arxiv.org/abs/2604.05940

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