稳定化方法与后稳定化方法的比较

A Comparision between Stabilization and Post-Stabilization

对BaumgaLrte的稳定化和Chin的后稳定化进行了详尽讨论与数值比较．用经典数值方法并结合这两种稳定化方式都能提高数值精度和改善数值稳定性．在最佳稳定参数下稳定化精度一般不等价于后稳定化．两者精度优劣并无常定．考虑到Baumgarte的稳定化使得数值积分的右函数更复杂和增加计算耗费,尤其是存在稳定参数最佳选取的麻烦,故推荐后稳定化投入实算．但值得注意的是用后稳定化与没有经过稳定化处理的经典积分器来比不宜扩大积分步长．

A discussion and a comparison between Baumgarte＇s stabilization method and Chin＇s post-stabilization one are given in detail. It is shown that classical numerical methods with the two stabilization ways can achieve higher accuracy and improve numerical stability. As an emphasis, the former is not equivalent to the latter in general even if the best stabilizing parameter can be found. In addition, it is ambiguous to deduce whether the former is or not superior to the latter from the accuracy point of view for various problems. On the other hand, it is clear that the stabilization leads to the appearance of a complicated right function so that the computation of the right function becomes more expensive. Above all, there is a difficulty in choosing the best stabilizing parameter. In view of these factors, the post-stabilization is worth recommending in many cases. However, a noticeable problem should be mentioned that for the post-stabilization employing larger time step size is inadvisable but for the traditional integrator the use of time step size has allowance of appropriate expanding.