Binary Interaction Approximation to N-Body Problems

Abstract

The binary interaction approximation (BIA) to N-body problems is proposed. The BIA conserves total linear momenta in principle. Other invariants, such as the total angular momentum and total energy, are conserved to at least 12 effective digits for a two-dimensional hydrogen plasma of T = 10 keV and n = 10²⁰ m⁻³. For such a plasma, the total CPU time of the BIA is found to scale as approximately N^1.9, while the conventional direct integration method scales as approximately N³.