Post-Newtonian behavior of the Bondi mass

We present an algorithm for calculating the Bondi mass, based upon renormalized variables, which converges at second order in grid size. The algorithm is highly effective in exploring both the Newtonian and strong field limits of general relativity. In particular, we study a quasi-Newtonian system with gravitational radiation. The algorithm allows calculation of the Newtonian mass and mechanical energy and joins smoothly to a post-Newtonian expansion of the Bondi mass carried out through terms of $O\left({\lambda }^7\right)$. At higher $\lambda$, the computed mass peels away and shows markedly non-Newtonian behavior. It remains strictly positive, in contrast to the post-Newtonian expansion.