Abstract:
The integration of Newton's equations of motion for self-gravitating systems, particularly in the context of our Solar System's evolution, remains a paradigm for complex dynamics. We implement Stormer's multistep method in backward difference, summed form and perform arithmetic according to what we call "significance ordered computation". We achieve results where the truncation error of our thirteenth order integrator resides below machine (double) precision and roundoff error accumulation is strictly random and not systematic.