渐近理论

子路

请问有谁用过渐近理论的方法来求解物面上的源汇分布问题，并且它的外部解、内不解是怎么回事？在那些地方可以查阅到渐近理论的相关资料？

tianyer

就是摄动法吧

子路

非常感谢楼上兄弟的参与。
  摄动理论是可以求解的，只是因为小弟前不久看到一篇文章用到此方法来求解，但有点看不懂。因此，想看看基本的东西。不知那位大虾看到过这方面的文章，请指点一下。

子路

用的是摄动方法，但求解势函数时用的是渐近理论。

windsnow

If we expand a function f(x) into a CONVERGING series by a perturbation method, say,
f(x) = f_0 + f_1 + f_2 + f_3 + f_4 + … + f_200 + f_201 + f_202 + … + f_n + …,
f_n will rapidly approach 0 as n approaches infinity (because it is a converging series). However, it will not help very much in practice if the major contributions to f(x) come from the middle terms, say, from f_200, f_201, and f_202, rather than from the first few terms, say, f_0 and f_1. The asymptotic expansion is a special perturbation method of the important property that the leading term is roughly correct and further terms are corrections of decreasing size.
A brief and concise textbook on both the asymptotic theory and other popular perturbation methods is:
Hinch, E. J., 1991: Perturbation Methods. Cambridge Univ. Press, Cambridge, 160 pp.