NUMERICAL-ANALYSIS OF THE SYMMETRICAL METHODS

Aimed at the initial value problem of the particular second-order ordi nary differential equations, y'' = f(x, y), the symmetric methods (Qui nlan and Tremaine, 1990) and our methods (Xu and Zhang, 1994) have bee n compared in detail by integrating the artificial earth satellite orb its in this paper. In the end, we point out clearly that the integral accuracy of numerical integration of the satellite orbits by applying our methods is obviously higher than that by applying the same order f ormula of the symmetric methods when the integration time-interval is not greater than 12000 periods.