Astronomy and Astrophysics – Astronomy
Scientific paper
Mar 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001aj....121.1768f&link_type=abstract
The Astronomical Journal, Volume 121, Issue 3, pp. 1768-1775.
Astronomy and Astrophysics
Astronomy
2
Celestial Mechanics, Methods: Numerical, Solar System: General
Scientific paper
Three approaches to reduce the accumulation of round-off errors in symplectic integrators are examined. The first is to reduce the number of summations in the implementation of symplectic algorithms. Although the effect is small, around a 30% reduction of accumulated round-off error, its use is always recommended because it is achieved with no extra computational time. The second approach is the use of Dekker's 1971 double-length addition routine in the main summation procedure. It provides a result that is a few digits more precise for less than a 25% increase in computational time. The third is the full application of Dekker's double-length routine library to the whole procedure, including the force evaluation. This realizes a quasi-quadruple-precision integration at a cost of a 6-13 times increase in CPU time, which is still 4-23 times faster than full quadruple-precision computation. All these reductions of round-off error depend little on the order of the symplectic integrator. Unfortunately, the last two approaches will not be applicable to mixed-variable symplectic integrators unless double-length routines to evaluate trigonometric functions are developed.
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