Hostname: page-component-6bf8c574d5-n2sc8 Total loading time: 0 Render date: 2025-03-07T06:20:59.095Z Has data issue: false hasContentIssue false
  • English
  • Français

Errors in numerical integrations and chaotic motions

Published online by Cambridge University Press:  12 April 2016

A. Milani  and
A.M. Nobili
A. Milani
Affiliation:
Universita’ di Pisa, Dipartimento di Matematica, Piazza dei Cavalieri 2, I-56100 Pisa, Italy
A.M. Nobili
Affiliation:
Universita’ di Pisa, Dipartimento di Matematica, Piazza dei Cavalieri 2, I-56100 Pisa, Italy

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The methods to estimate the integration errors, including the effects of truncation, rounding off, and instability of the solutions, are discussed. Polynomial error accumulation depends upon numerical method, stepsize, orbital period and also eccentricity; it is also machine dependent. Comets correspond to the most difficult case of exponentially diverging orbits; however they can be very close to resonant ordered regions.

Type
Section IV. Dynamics of Comets: Numerical Modelling
Information
International Astronomical Union Colloquium , Volume 83: Dynamics of Comets: Their Origin and Evolution , 1985 , pp. 215 - 226
Copyright
Copyright © Cambridge University Press 1985

References

Arnold, V.l. (1963) Usp. Mat. Nauk. 18, 91.Google Scholar
Benettin, G., Galgani, L., Giorgilli, A. and Strelcyn, J.M. (1980) Meccanica, March 1980, 9.Google Scholar
Brouwer, D. (1937) Astr. J. 46, 149.Google Scholar
Fabri, E. and Penco, U. (1984) “Propagation of the Round-off Errors in Numerical Integrations”, in preparation.Google Scholar
Heinrici, P. (1962) Discrete Variable Methods in Ordinary Differential Equations, John Wily & Sons, New York-London.Google Scholar
Henon, M. and Helies, C. (1964) Astron. J. 69, 73.Google Scholar
Kinoshita, H. (1968) Pubbl. Astr. Soc. Japan 20, 1.Google Scholar
Kovalevsky, J. (1963) Introduction a la mecanique celeste, Armand Colin, Paris.Google Scholar
Milani, A. and Nobili, A.M. (1984a) Celestial Mechanics, in press.Google Scholar
Milani, A. and Nobili, A.M. (1984b) Astron. Astrophys., in press.Google Scholar
Smale, S. (1967) Bull. A.M.S. 73, 747.CrossRefGoogle Scholar
Wintner, A. (1941) The Analytical Foundations of Celestial Mechanics, Princeton Univ. Press. Google Scholar
Cohen, C.J., Hubbard, E.C. and Oesterwinter, C. (1973) Astr. Pap. Am. Ephem. 22, pt. 1.Google Scholar