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A time-transformed leapfrog scheme. Integration of few-body systems with large mass ratios. (English) Zbl 1026.70003

Summary: We present a time-transformed leapfrog scheme combined with the extrapolation method to construct an integrator for orbits in \(N\)-body systems with large mass ratios. The basic idea can be used to transform any second-order differential equation into a form which may allow more efficient numerical integration. When applied to gravitating few-body systems, this formulation permits extremely close two-body encounters to be considered without significant loss of accuracy. The new scheme has been implemented in a direct \(N\)-body code for simulations of super-massive binaries in galactic nuclei. In this context relativistic effects may also be included.

MSC:

70-08 Computational methods for problems pertaining to mechanics of particles and systems
70F10 \(n\)-body problems

Software:

NBODY6; NBODY4
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