论文标题
具有转折点的不均匀微分方程的渐近解决方案
Asymptotic solutions of inhomogeneous differential equations having a turning point
论文作者
论文摘要
渐近溶液是针对具有较大的真实或复杂参数和简单转折点的不均匀微分方程的。它们涉及得分手功能和三个缓慢变化的分析系数函数。渐近近似对于参数的无限复杂值均匀地有效，并应用于具有多项式和指数强迫项的不均匀的通风方程。所有近似值都可以使用误差界，包括大型复杂参数的得分手函数的新简单渐近范围。
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The asymptotic approximations are uniformly valid for unbounded complex values of the argument, and are applied to inhomogeneous Airy equations having polynomial and exponential forcing terms. Error bounds are available for all approximations, including new simple ones for the well-known asymptotic expansions of Scorer functions of large complex argument.
