term numerical integrations seem to have been performed with very small errors. the averaged relative errors of total energy (～10?9) and of total angular momentum (～10?11) have remained nearly constant throughout the integration period (fig. 1). the special startup procedure， warm start， would have reduced the averaged relative error in total energy by about one order of magnitude or more.
relative numerical error of the total angular momentum δa/a0 and the total energy δe/e0 in our numer