Power-elliptic expansions of solutions to an ordinary differential equation

被引：0
|
作者：
A. D. Bruno
机构：
[1] Russian Academy of Sciences,Keldysh Institute of Applied Mathematics
来源：
Computational Mathematics and Mathematical Physics | 2012年 / 52卷
关键词：
ordinary differential equation; asymptotic expansion of solutions; elliptic asymptotic behavior; first and second Painlevé equations;
D O I：
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学科分类号：
摘要：
A rather general ordinary differential equation is considered that can be represented as a polynomial in variables and derivatives. For this equation, the concept of power-elliptic expansions of its solutions is introduced and a method for computing them is described. It is shown that such expansions of solutions exist for the first and second Painlevé equations.
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页码：1650 / 1661
页数：11
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