具有两个转向点的大参数奇摄动方程的渐近解

欧阳成;韩祥临

系统科学与数学 ›› 2011, Vol. 31 ›› Issue (1) : 41-047.

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系统科学与数学 ›› 2011, Vol. 31 ›› Issue (1) : 41-047. DOI: 10.12341/jssms09449
论文

具有两个转向点的大参数奇摄动方程的渐近解

    欧阳成, 韩祥临
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Asymptotic Solutions of Singularly Perturbed Equations for Large Parameter with Two Turning Points

    OUYANG Cheng, HAN Xianglin
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摘要

利用匹配法研究了一类具有两个转向点的大参数奇摄动方程,通过Liouville-Green变换和Airy函数分别构造了方程在不同区域的外部解和内层解,得出了方程的渐近解,即解在不同范围内的5个渐近表达式及其5对常数之间的4个匹配条件.

Abstract

Using the matching method, a class of singularly perturbed equations for large
parameter with two turning points is discussed. The outer solutions and the interior layer solutions of the equations in different region are constructed respectively by Liouville-Green transformation and Airy function. The asymptotic solutions, i.e. five asymptotic expansions in different range, of the equations and four matching conditions among their five pairs of constants are obtained.

关键词

奇摄动 / 转向点 / 外部解 / 内层解 / 匹配.

Key words

Singular perturbation / turning point / outer solution / interior layer solution / matching.

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欧阳成 , 韩祥临. 具有两个转向点的大参数奇摄动方程的渐近解. 系统科学与数学, 2011, 31(1): 41-047. https://doi.org/10.12341/jssms09449
OUYANG Cheng , HAN Xianglin. Asymptotic Solutions of Singularly Perturbed Equations for Large Parameter with Two Turning Points. Journal of Systems Science and Mathematical Sciences, 2011, 31(1): 41-047 https://doi.org/10.12341/jssms09449
中图分类号： 34E20    34B15   
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