Abstract: The asteroids are the most important small bodies in the solar system,and they mainly lies in the two locations-a main belt between the Mars's orbit and the Jupiter's and the near Earth space.The most feature of the orbits of Near Earth Asteroids (NEAs) is that the semi major axes of the orbits are nearly equal to that of the Earth or the perihelia distances are approximate to or even less than the mean distance between the Sun and the Earth,thus they could move into inside of the Earth's orbit,so that they might close approach or even colliside with the Earth (or other planets,such as the Venus,the Mars,etc.).The characteristic brings about some difficulties in the numerical research during their orbital evolution,which leads to the failure of the normalization technique in the general removal impact singularities of celestial mechanics methods and the Symplectic Algorithm which is successfully applied to the investigation in quality.By comparing the computation effects of several common numerical methods (including Symplectic Algorithm),and considering the nature of the movement of the small bodies,the corresponding treatments are provided here to improve the reliability of the computation.

Key words: main belt asteroids, Near Earth Asteroids, orbital evolution, numerical method