标题： 米尔恩相位-振幅方程的显式数值格式 显示英文标题

标题： An explicit numerical scheme for Milne's phase-amplitude equations

摘要： 我们提出了一种显式数值方法来求解Milne的相位-振幅方程。之前提出的方法直接求解Milne的非线性振幅方程。因此，它们对误差非常敏感，并且容易由于振幅的虚假快速变化成分的增长而产生不稳定性。这使得系统地使用这些方法变得困难。相反，目前的方法是基于求解一个与非线性振幅方程等价的线性三阶方程。这个线性方程是由Kiyokawa推导出来的，他用它来获得关于库仑波函数的解析结果[Kiyokawa, AIP Advances, 2015]。目前的方法用于数值计算，从而解决了快速变化成分增长的问题。 显示英文摘要

摘要： We propose an explicit numerical method to solve Milne's phase-amplitude equations. Previously proposed methods solve directly Milne's nonlinear equation for the amplitude. For that reason, they exhibit high sensitivity to errors and are prone to instability through the growth of a spurious, rapidly varying component of the amplitude. This makes the systematic use of these methods difficult. On the contrary, the present method is based on solving a linear third-order equation which is equivalent to the nonlinear amplitude equation. This linear equation was derived by Kiyokawa, who used it to obtain analytical results on Coulomb wavefunctions [Kiyokawa, AIP Advances, 2015]. The present method uses this linear equation for numerical computation, thus resolving the problem of the growth of a rapidly varying component.