Abstract
Possible sources of roundoff error in solar system integrations are studied. It is suggested than when floating point arithmetic is optimal, the majority of roundoff error arises from two sources: the approximate representation of the numerical coefficients used in multistep integration formulas and the additions required to evaluate these formulas. An algorithm to remove these two sources of error in computers with optimal arithmetic is presented. It is shown that the corrections result in a substantial reduction in the energy error at the cost of less than a factor of 2 increase in computing time.
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