Taisei Asai, Hisatoshi Kodani, Kaname Matsue, Hiroyuki Ochiai, Takiko Sasaki
Nonlinearity, 38(4) 045003-045003, Apr 30, 2025 Peer-reviewed
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. 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.