Convergence Behaviors of a Post-Minkowskian N-Body Code in the Regime of Two-Body Interactions

A Post-Minkowskian N-body code, with computational complexity scaling of N2 and quadruple precision, was written using the closed form Hamiltonian derived by Ledvinka et al. (2008).12 While the code has been written to handle an arbitrary number of particles, the scaling limits the number of particles in practice. The code uses a fourth-order Runge-Kutta integration method, which is applied to Hamilton’s equations to form a set of 2N first-order, coupled ODEs. It was shown that the code numerically converges to unique solutions for two-body interactions in the Newtonian regime and the relativistic regime. The analytical solutions are discussed afterwards.