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arXiv · 2211.06865

Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. I -- Method and Justification

Taisei Asai·Hisatoshi Kodani·Kaname Matsue·Hiroyuki Ochiai·Takiko Sasaki
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Abstract

In this paper, we provide a systematic methodology for calculating multi-order asymptotic expansion of blow-up solutions near blow-up for autonomous ordinary differential equations (ODEs). Under the specific form of the principal term of blow-up solutions for a class of vector fields, we extract algebraic objects determining all possible orders in the asymptotic expansions. Examples for calculating concrete multi-order asymptotic expansions of blow-up solutions are finally collected.

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Taisei Asai, Hisatoshi Kodani, Kaname Matsue, Hiroyuki Ochiai, Takiko Sasaki. 2022-11-13. Multi-order asymptotic expansion of blow-up solutions for autonomous ODEs. I -- Method and Justification. https://arxiv.org/abs/2211.06865

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