Mikkola, Seppo; Aarseth, Sverre A time-transformed leapfrog scheme. Integration of few-body systems with large mass ratios. (English) Zbl 1026.70003 Celest. Mech. Dyn. Astron. 84, No. 4, 343-354 (2002). 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. Cited in 7 Documents MSC: 70-08 Computational methods for problems pertaining to mechanics of particles and systems 70F10 \(n\)-body problems Keywords:time transformations; second-order differential equations; composite integration; \(N\)-body problem; leapfrog scheme Software:NBODY6; NBODY4 PDFBibTeX XMLCite \textit{S. Mikkola} and \textit{S. Aarseth}, Celest. Mech. Dyn. Astron. 84, No. 4, 343--354 (2002; Zbl 1026.70003) Full Text: DOI