Accurate and precise N-body simulations

Tjarda Boekholt (University of Aveiro)

September 20, 2018

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Abstract: Numerical solutions to Newton’s equations of motion for chaotic self gravitating systems are often regarded to be irreversible. This is due to the exponential growth of irreversible numerical errors. We demonstrate that when numerical errors are reduced to below an initial physical perturbation and its exponential growth during integration the microscopic reversibility is retrieved. Time reversibility itself is not a guarantee for a definitive solution to the chaotic N-body problem. However, time reversible algorithms may be used to find initial conditions for which perturbed trajectories converge rather than diverge. The ability to calculate such a converging pair of solutions is a striking illustration which shows that it is possible to compute a definitive solution to a highly unstable problem. This works as follows: If you (i) use a code which is capable of producing a definitive solution (and which will therefore handle converging pairs of solutions correctly), (ii) use it to study the statistical result of some other problem, and then (iii) find that some other code produces a solution S with statistical properties which are indistinguishable from those of the definitive solution, then solution S may be deemed veracious.