ANZIAM J. 46(E) pp.C786--C804, 2005.

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

K. R. Grazier

W. I. Newman

James M. Hyman

Philip W. Sharp

David J. Goldstein
(Received 28 October 2004, revised 13 July 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 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.

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Authors

K. R. Grazier
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA. mailto:krg@anlashok.jpl.nasa.gov
W. I. Newman
Departments of Earth & Space Sciences, Physics & Astronomy, and Mathematics, University of California, Los Angeles, CA 90095-1567, USA. mailto:win@ucla.edu
James M. Hyman
Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. mailto:mac@t7.lanl.gov
Philip W. Sharp
Department of Mathematics, Private Bag 92019, Auckland, New Zealand. mailto:sharp@math.auckland.ac.nz
David J. Goldstein
Consultant, Culver City, CA, USA. mailto:acwdjg@comcast.net

Published August 23, 2005. ISSN 1446-8735

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Copyright Austral. Mathematical Soc.; prepared August 23, 2005, from Graz.tex with anziamje.sty (v2.3h)