Alexander, M. E. Simulation of binary-single star and binary-binary scattering. (English) Zbl 0585.65055 J. Comput. Phys. 64, 195-219 (1986). Numerical methods for integrating gravitational 3- and 4-body systems are investigated and tested. The methods employ multiple-pair regularization schemes for N-body systems which use the Kustaanheimo-Stiefel transformation for regularizing 2-body collisions, in conjunction with a number of different time transformations between ”physical” and ”parameter” time. These transformations can be chosen so as to make the singularity in the equations of motion, caused by many-body collisions, as mild as possible. The various time transformations are tested on both 3- and 4-body systems by comparing the numerical with known analytical solutions, and by time reversal of the integrations through many-body close encounters. Computer programs for binary-single star and binary- binary scattering have been developed and are described. They can be used in an extensive project for determining scattering cross sections with any of the above methods. They are used here to compare the performance of these methods, for a fixed set of initial conditions, on scattering involving ”hard” binaries, in which strong resonances can occur. It is found that the outcome of the scattering, for example, the identity of the escaping particle(s), can vary with method, thus reflecting the inherent instability of the N-body problem. Cited in 1 ReviewCited in 3 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 70F10 \(n\)-body problems 70-08 Computational methods for problems pertaining to mechanics of particles and systems 70F05 Two-body problems 70F07 Three-body problems 85A05 Galactic and stellar dynamics 65L07 Numerical investigation of stability of solutions to ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 70F35 Collision of rigid or pseudo-rigid bodies 70-04 Software, source code, etc. for problems pertaining to mechanics of particles and systems Keywords:binary-binary scattering; gravitational 3- and 4-body systems; Kustaanheimo-Stiefel transformation; 2-body collisions; time transformations; instability PDFBibTeX XMLCite \textit{M. E. Alexander}, J. Comput. Phys. 64, 195--219 (1986; Zbl 0585.65055) Full Text: DOI References: [1] Aarseth, S. 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