Reduction of round-off errors in the extrapolation methods and its application to the integration of orbital motion

A simple technique to reduce round-off errors was applied to the extrapolation methods to integrate ordinary differential equations. The methods with this technique are always superior to the original methods. The required computational labor remains almost the same. Numerical simulations showed that the new methods provide a few digits more precise results than the original methods. Alternatively, the new methods run roughly twice as fast as the original methods if the same accuracy is required. (C) 1996 American Astronomical Society.