egration 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 numerical integrationsn± 1，2，3， where δe and δa are the absolute change of the total energy and total angular momentum， respectively， ande0anda0are their initial values. the horizontal unit is gyr.
note that different operating systems， different mathematical libraries， and different hardware architectures result in different numerical errors， through the variations in round-
对火星轨道变化问题的最后解释(18/49)