常微分方程数值解法在动力天文中的应用

在动力天文中,利用常微数值解法求解运动方程时,通常会出现两个问题——解的定性性质受到歪曲和轨道沿迹误差的严重累积。本文将介绍利用运动本身的一些力学性质作为控制条件,能够有效地解决这些问题,特别是对Hamiltom系统,采用保持辛结构的差分格式——半积分器(Symplectic Imtegrators),有它独特的优点,而且可以将相应的差分格式稍作修改,就可用于小耗散系统,这对动力天文而言也是很重要的。

Applications of Numerical Methods of O. D. E. to Dynamic Astronomy

In the procedure of solving the motional equations of dynamical astronomy by using numerical methods of ordinary differential equations, we will meet generally two problems: the qualitative properties of the solution are distorted and the accumulation of orbital along-track error is very serious. In this paper, we use the intrinsic dynamic properties of the motions as control conditions to settle effectively the above problems. Especially, for a Harniltonian system, the difference scheme of preserving symplectic structure, i.e. symplectic integrator- display a distinctive advantage for the above problems. Symplectic integrators can also be extended to small dissipative systems so long as a little modifications are done in the symplectic difference schemes, this is very important to the researches on dynamical astronomv.