Last years many scientists used symplectic integrators , which are much faster than usual integrators. For asteroids, a step of integration for a symplectic integrator usually was taken in a range between 7 and 30 days. Some scientists compared the results obtained with different integration steps, but usually they did not compare these results with those obtained with a usual integrator. We have made series of computer runs of the orbital evolution of asteroids for the 3/1 and 5/2 resonances with Jupiter using both the symplectic integrator RMVS3  and the Bulirsh-Stoer method  (BULSTO). The results obtained with different integrators and different integration steps ds were compared in order to understand what error we usually make if we use a symplectic method for investigations of orbital evolution of resonant main-belt asteroids. For BULSTO the error ε per integration step was taken to be less than 10 −8 or 10 −9. For RMVS3, we have made integrations with ds equal to 3, 10, and 30 days. In each run we considered the Sun, 7 planets (except Mercury and Pluto) and N asteroids moving in the 3/1 or 5/2 resonances with Jupiter (a◦=2.5 or a◦=2.823 AU). Initial eccentricities and inclinations were the same in all runs: e◦=0.15 and i◦=10 ◦. Initial values of the mean anomaly and the longitude of the ascending node were different. The considered time interval TS equaled severa
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.