Numerical validation of blow-up solutions of ordinary differential equations

Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shinichi Oishi

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This paper focuses on blow-up solutions of ordinary differential equations (ODEs). We present a method for validating blow-up solutions and their blow-up times, which is based on compactifications and the Lyapunov function validation method. The necessary criteria for this construction can be verified using interval arithmetic techniques. Some numerical examples are presented to demonstrate the applicability of our method.

Original languageEnglish
Pages (from-to)10-29
Number of pages20
JournalJournal of Computational and Applied Mathematics
Volume314
DOIs
Publication statusPublished - 2017 Apr 1

Fingerprint

Blow-up of Solutions
Lyapunov functions
Ordinary differential equations
Ordinary differential equation
Blow-up Time
Interval Arithmetic
Blow-up Solution
Compactification
Lyapunov Function
Numerical Examples
Necessary
Demonstrate

Keywords

  • Blow-up solutions
  • Compactifications
  • Lyapunov functions
  • Ordinary differential equations
  • Validated computations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Numerical validation of blow-up solutions of ordinary differential equations. / Takayasu, Akitoshi; Matsue, Kaname; Sasaki, Takiko; Tanaka, Kazuaki; Mizuguchi, Makoto; Oishi, Shinichi.

In: Journal of Computational and Applied Mathematics, Vol. 314, 01.04.2017, p. 10-29.

Research output: Contribution to journalArticle

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