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Cite Details

K. R. Grazier, W. I. Newman, David J. Goldstein, James M. Hyman and Philip W. Sharp, "Brouwer's Law: Optimal Multistep Integrators for Celestial Mechanics", Preprint: LA-UR-05-2277, 2005

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 Störmer'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 out order thirteen integrator resides below machine (double) precision and roundoff error accumulation is strictly random and not systematic.

BibTeX Entry

@unpublished{grazier-2005-Brouwer,
author = {K. R. Grazier and W. I. Newman and David J. Goldstein and James M. Hyman and Philip W. Sharp},
title = {Brouwer's Law: Optimal Multistep Integrators for Celestial Mechanics},
year = {2005},
urlpdf = {http://math.lanl.gov/~mac/papers/numerics/GNGHS05.pdf},
note = {Preprint: LA-UR-05-2277}
}