Round-off error in long-term orbital integrations using multistep methods

Techniques for reducing roundoff error are compared by testing them on high-order Störmer and summetric multistep methods. The best technique for most applications is to write the equation in summed, function-evaluation form and to store the coefficients as rational numbers. A larger error reduction can be achieved by writing the equation in backward-difference form and performing some of the additions in extended precision, but this entails a larger cpu cost.