Cowell数值积分器的变步长与自起步方法

Cowell多步法积分器简单易用、计算高效,但也存在着步长变换困难和积分起步需借助其他工具等缺点,限制了其应用范围。为了使Cowell积分器更加方便实用,可以处理更多的问题,对积分器实现了以下3个方面的改进:首先实现了无精度损失的变步长操作,经实际验算,即便经过几十万次的反复步长变换,计算精度也没有损失;其次利用逐阶迭代的方式实现了积分器的自起步,摆脱了对其他工具的依赖;最后推荐了一种增加和分值存储字长的方法来减小舍入误差,误差减小效果显著,积分10~9圈以后相对误差仍小于1%。

The Method of Step Size Change and Self-startup of Cowell Integrator

The multistep integrator with equal-space is easy to use and efficient, but difficult to change the step size and to realize the self-start process, so that the application scope of integrator is limited. In order to make Cowell integrator more convenient and handle more problems, the following three aspects of integrator are improved: Firstly, a method is provided to change the step size without any additional error created, through practical calculation, even after hundreds of thousands of times of repeated step transformation, there is no loss of calculation accuracy. Secondly, the self-starting of integrator is realized by the way of order-by-order iteration, and the dependence on other tools is eliminated. At last, a method to reduce rounding error is recommended by increasing and storing word length with significant effect on error reduction, and the relative error is still less than 1% after integrating 1E+9 cycles.