辛四阶映射用于碰撞性N体问题
Symplectic fourth-order maps for the collisional N-body problem
AI总结：
本文研究了采用开普勒求解器处理 pairwise 交互的辛且时间可逆的 N-body 积分器，通过修正二阶误差获得四阶方案，并推广为仅对部分交互使用开普勒求解器仍保持四阶精度的积分器。
摘要：
我们分析和实验研究了某些辛且时间可逆的 N-body 积分器，这些积分器对每对相互作用使用开普勒求解器，包括 Hernandez & Bertschinger (2015) 的方法。由于开普勒求解器，这些方法能正确处理近距离两体相互作用，而近距离三体相遇则对截断误差产生二次及更高阶的影响。二阶误差可通过少量计算开销修正以获得四阶方案。我们推广此映射为一种仅对部分相互作用使用开普勒求解器但仍保持四阶精度的积分器。在这种情况下，未通过开普勒求解器处理的两体相遇则会贡献截断误差。
英文摘要：
We study analytically and experimentally certain symplectic and time-reversible N-body integrators which employ a Kepler solver for each pair-wise interaction, including the method of Hernandez & Bertschinger (2015). Owing to the Kepler solver, these methods treat close two-body interactions correctly, while close three-body encounters contribute to the truncation error at second order and above. The second-order errors can be corrected to obtain a fourth-order scheme with little computational overhead. We generalise this map to an integrator which employs a Kepler solver only for selected interactions and yet retains fourth-order accuracy without backward steps. In this case, however, two-body encounters not treated via a Kepler solver contribute to the truncation error.
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