Error and long-term analysis of two-step symmetric methods for relativistic charged-particle dynamics
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912570082852864 |
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| author | Li, Ting Wang, Bin Zhang, Ruili |
| author_facet | Li, Ting Wang, Bin Zhang, Ruili |
| contents | In this work, we consider the error estimates and the long-time conservation or near-conservation of geometric structures, including energy, mass shell and phase-space volume, for four two-step symmetric methods applied to relativistic charged-particle dynamics. We begin by introducing a two-step symmetric numerical method based on a splitting scheme that exactly preserves the mass shell and the phase-space volume of the relativistic system. Building on this formulation, we develop three additional two-step symmetric methods with further modifications, for which the long-time near-conservation of energy and mass shell can be rigorously established through the backward error analysis. All methods are shown to achieve second-order accuracy. The theoretical results are illustrated and complemented by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03886 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error and long-term analysis of two-step symmetric methods for relativistic charged-particle dynamics Li, Ting Wang, Bin Zhang, Ruili Numerical Analysis In this work, we consider the error estimates and the long-time conservation or near-conservation of geometric structures, including energy, mass shell and phase-space volume, for four two-step symmetric methods applied to relativistic charged-particle dynamics. We begin by introducing a two-step symmetric numerical method based on a splitting scheme that exactly preserves the mass shell and the phase-space volume of the relativistic system. Building on this formulation, we develop three additional two-step symmetric methods with further modifications, for which the long-time near-conservation of energy and mass shell can be rigorously established through the backward error analysis. All methods are shown to achieve second-order accuracy. The theoretical results are illustrated and complemented by numerical experiments. |
| title | Error and long-term analysis of two-step symmetric methods for relativistic charged-particle dynamics |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2509.03886 |