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arXiv · 1609.09375

Symplectic fourth-order maps for the collisional N-body problem

Walter Dehnen·David M. Hernandez
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Abstract

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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Walter Dehnen, David M. Hernandez. 2016-09-29. Symplectic fourth-order maps for the collisional N-body problem. https://doi.org/10.1093/mnras%2Fstw2758

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