广义Airy函数与具有n个转向点的方程

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Extended Airy Function and Differential Equations with n-Turning Points

摘要: 本文研究二阶线性常微分方程其中为大参数,即方程n个转向点.本文使用匹配法,对三个转向点的情况,进行详细分析研究,得到形式一致有效渐近解,并阐明对n个转向点的情况,方法也是一样的.
- 一致有效的 /
- 渐近解 /
- 转向点
Abstract: This paper studies a second order linear ordinary differential equation with n-turning points Where q₁=(x-µ₁)(x-µ₂)…(x-µ_n)ƒ(x)≠0,and λ is a large parameter.The formal uniformly valid asymptotic solution of the equation is obtained based on the analysis of the three points by means of the matched method.By the work a method is developed and the applicability of this method to the n-turning points is demonstrated.
- Uniformly valid /
- asymptotic solution /
- turning point

[1]	蒲富全,具有二阶转向点方程的一致有效渐近解问题.清华大学学报.20(3)(1980),103-109.
[2]	郭敦仁.《数学物理方程》,人民出版社(1979).
[3]	Olver,F.W.J.,Asymptotics and Special Function(1974).
[4]	Nayfeh,A.H.,Perturbation Methods(1973).
[5]	Sibuya,Y.,Global Theory of a Second Order Linear Ordinary Differential Equatin with a Polynomial Coefficient,North-Holland Publishing Company(1975).

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