NEW METHOD FOR THE NUMERICAL-INTEGRATION OF AN N-BODY SYSTEM IN AN EXTERNAL POTENTIAL

A newly developed numerical-integration method is presented. It has a great advantage when used to numerically calculate the orbital motion of mutually interacting planetesimals in a strong external (the solar gravitational) field. In an ordinary difference scheme, since the effe ct of a weak mutual gravity would be embedded in the truncation error of the strong solar gravity, we cannot reflect the small, but importan t, effect of mutual gravity on the numerical calculation. Our new meth od helps us to overcome this difficulty by suppressing the truncation error of numerical integration. The essence of our method is to expres s a solution as a sum of unperturbed and perturbed solutions: the form er represents the motion only under an external field; the latter repr esents a small deviation from an unperturbed orbit due to mutual gravi ty between planetesimals. The perturbed solution is found by means of an ordinary integrator, whereas an unperturbed solution is sought by a higher-order integrator (or, by an analytical manner). By this method , we can integrate orbits both accurately and speedily. Since our meth od has a very simple algorithm, we can apply it to well-known numerica l integration methods, such as the Runge-Kutta method and the Predicto r-Corrector method.