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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

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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

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