An adaptive symplectic integrator for gravitational dynamics
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913950114775040 |
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| author | Ye, Keqi Cai, Zizhe Wang, Mingji Yang, Kun Liu, Xiaodong |
| author_facet | Ye, Keqi Cai, Zizhe Wang, Mingji Yang, Kun Liu, Xiaodong |
| contents | This paper presents an adaptive symplectic integrator, SQQ-PTQ, developed on the basis of the fixed-step symplectic integrator SQQ. To mitigate the Runge phenomenon, SQQ-PTQ employs Chebyshev interpolation for approximating the action, enhancing both the precision and stability of the interpolation. In addition, to reduce the computational cost of evaluating interpolation functions, SQQ-PTQ introduces a projection method that improves the efficiency of these computations. A key feature of SQQ-PTQ is its use of the time transformation to implement an adaptive time step. To address the challenge of computing complicated Jacobian matrices attributed to the time transformation, SQQ-PTQ adopts a quasi-Newton method based on Broyden's method. This strategy accelerates the solution of nonlinear equations, thereby improving the overall computational performance. The effectiveness and robustness of SQQ-PTQ are demonstrated via three numerical experiments. In particular, SQQ-PTQ demonstrates adaptability in handling close-encounter problems. Moreover, during long-term integrations, SQQ-PTQ maintains the energy conservation, further confirming its advantages as a symplectic algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14881 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An adaptive symplectic integrator for gravitational dynamics Ye, Keqi Cai, Zizhe Wang, Mingji Yang, Kun Liu, Xiaodong Numerical Analysis Astrophysics of Galaxies This paper presents an adaptive symplectic integrator, SQQ-PTQ, developed on the basis of the fixed-step symplectic integrator SQQ. To mitigate the Runge phenomenon, SQQ-PTQ employs Chebyshev interpolation for approximating the action, enhancing both the precision and stability of the interpolation. In addition, to reduce the computational cost of evaluating interpolation functions, SQQ-PTQ introduces a projection method that improves the efficiency of these computations. A key feature of SQQ-PTQ is its use of the time transformation to implement an adaptive time step. To address the challenge of computing complicated Jacobian matrices attributed to the time transformation, SQQ-PTQ adopts a quasi-Newton method based on Broyden's method. This strategy accelerates the solution of nonlinear equations, thereby improving the overall computational performance. The effectiveness and robustness of SQQ-PTQ are demonstrated via three numerical experiments. In particular, SQQ-PTQ demonstrates adaptability in handling close-encounter problems. Moreover, during long-term integrations, SQQ-PTQ maintains the energy conservation, further confirming its advantages as a symplectic algorithm. |
| title | An adaptive symplectic integrator for gravitational dynamics |
| topic | Numerical Analysis Astrophysics of Galaxies |
| url | https://arxiv.org/abs/2507.14881 |