Efficient High-order Mass-conserving and Energy-balancing Schemes for Schrödinger-Poisson Equations
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arXiv
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| Format: | Preprint |
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2026
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| author | Rajvanshi, Manvendra Pratap Ketcheson, David I. |
| author_facet | Rajvanshi, Manvendra Pratap Ketcheson, David I. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_05940 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient High-order Mass-conserving and Energy-balancing Schemes for Schrödinger-Poisson Equations Rajvanshi, Manvendra Pratap Ketcheson, David I. Computational Physics Numerical Analysis 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. |
| title | Efficient High-order Mass-conserving and Energy-balancing Schemes for Schrödinger-Poisson Equations |
| topic | Computational Physics Numerical Analysis |
| url | https://arxiv.org/abs/2604.05940 |