Numerical validation of blow-up solutions with quasi-homogeneous compactifications

Kaname Matsue, Akitoshi Takayasu

研究成果: ジャーナルへの寄稿学術誌査読

2 被引用数 (Scopus)

抄録

We provide a numerical validation method of blow-up solutions for finite dimensional vector fields admitting asymptotic quasi-homogeneity at infinity. Our methodology is based on quasi-homogeneous compactifications containing quasi-parabolic-type and directional-type compactifications. Divergent solutions including blow-up solutions then correspond to global trajectories of associated vector fields with appropriate time-variable transformation tending to equilibria on invariant manifolds representing infinity. We combine standard methodology of rigorous numerical integration of differential equations with Lyapunov function validations around equilibria corresponding to divergent directions, which yields rigorous upper and lower bounds of blow-up time as well as rigorous profile enclosures of blow-up solutions.

本文言語英語
ページ(範囲)605-654
ページ数50
ジャーナルNumerische Mathematik
145
3
DOI
出版ステータス出版済み - 7月 1 2020

!!!All Science Journal Classification (ASJC) codes

  • 計算数学
  • 応用数学

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