插值摄动法及其在力学中的应用

Interpolation Perturbation Method and Its Application in Mechanics

本文研究了最高阶导数乘以小参数，或出现奇点的微分方程的定解问题，用插值摄动法求得了一级近似解，它和通常的奇异摄动法（匹配法、多尺度法）的一级近似解的精度相同。

In this paper, the authors study the boundary value problems of the differential equations, the highest order differentiation of which contains the small parameters or singular points. Using the interpolation perturbation method, we obtain the first order approximate solutions. It have the same precision as the first order approximate solutions obtained by the ordinary singular perturbation method.