Physics
Scientific paper
Dec 1972
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972cemec...6..468r&link_type=abstract
Celestial Mechanics, Volume 6, Issue 4, pp.468-482
Physics
8
Scientific paper
The integration by recurrent power series of certain differential equations occurring in celestial mechanics is shown to be very much more efficient and accurate than that produced by classical one step methods. It is shown that for any such system of differential equations the machine time taken to carry out an integration is a minimum for a certain choice of the number of terms taken in the recurrent power series. In the two-body orbits considered this number is about 15. For the same accuracy criterion the power series is faster than the Runge-Kutta method of the fourth order by a factor which varies between 6 and 15 depending on the eccentricity of the orbit.
Black William
Moran P. E.
Roy Archie E.
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