推荐数值求解y~″＝f（x，y）的几组积分系数

RECOMMENDATION OF A FEW GROUPS NUMERICAL INTEGRAL COEFFICIENTS FOR SOLVING THE DIFFERENTIAL EQUATIONS Y″=F(X, Y)

为求解特殊二阶常微分方程ｙ″＝（ｘ，ｙ）的初值问题，本文采用最大阶算子方法构造了一类线性多步积分公式，并与Ｃｏｗｅｌｌ方法的同阶公式作了大量的平行计算，通过对不同轨道类型、不同步长、不同积分间隔时的计算结果的全面仔细地分析比较，我们从八阶、十阶、十二阶、十四阶中各自选定一组积分系数，推荐给同行计算使用，结果表明，采用本文推荐的积分方法计算天体轨道是有益的，因为它的积分精度以及积分过程中误差累积的方式都十分明显地好于同阶的Ｃｏｗｅｌｌ方法。

In this paper, a series of linear multistep integration formulas are constructed for solving the initial value problem of the particular second order ordinary differential equations Y″=F(X,Y) by the method of Maximum Order Operator. The best four groups integration formulas are selected respectively from 8th-order, 10th-order,12th-order, 14th-order. The authors integrated respectively the same orbit of celestial body, using the same order formula of our method and the Cowell Method.We compared and analysised their calculation results for the different step length,or for the different Primary orbit elements, or for the different integration interval.We found integration accuracy of our method is higher obviously than the same order formulas of Cowell Method. Therefore it is suggested that our method might adapt to compute the orbit of celestial body.