基于Richardson外推的定步长Adams-Cowell改进积分方法

摘要

Aimming at the numerical solution of ordinary differential equations of the satellite, a fixed⁃stepsize Adams⁃Cowell numerical integration algorithm based on Richardson extrapolation is presented, Adams algorithm and Cowell algorithm is improved respectively. A detailed theoretical derivation is also proposed, and the general laws of the integration equations� coefficients with different orders are given in tabular form, which facilitates the engineering practice. Finally, spe⁃cific single differential equation and satellite orbit two⁃body equations are taken as examples to test this improved method, ac⁃cording to the simulation result, when compared with the un⁃improved method, the improved method presented here can reach to a higher precise, nearly one order of magnitude with some specific steps, the effectiveness of the improved method can be proved, this improved method can be used in engineering practice.%针对卫星轨道微分方程组的数值解法，提出了一种基于Richardson外推思想的定步长Adams⁃Cowell积分方法，分别对Adams方法和Cowell方法的PECE格式进行外推改进。结合外推改进的详细理论推导，总结出了不同阶积分公式的系数的数学规律，并以表格的形式给出，方便了工程实践。最后，利用卫星轨道二体运动方程对8阶改进的方法进行了仿真分析，由仿真结果可知，和未改进的算法相比，改进后的算法计算精度有了明显改进，在某些特定积分步长下的计算精度能提高一个数量级，证明了改进算法的有效性，此8阶改进的方法可用于工程实践。