Achieving Brouwer's law with high-order Stormer multistep methods

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 local truncation error of our order thirteen integrator resides below machine (double) precision and roundoff error accumulation is strictly random and not systematic.