On necessary and sufficient conditions for numerical verification of double turning points

Ken'ichiro Tanaka, Sunao Murashige, Shin'ichi Oishi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

This paper describes numerical verification of a double turning point of a nonlinear system using an extended system. To verify the existence of a double turning point, we need to prove that one of the solutions of the extended system corresponds to the double turning point. For that, we propose an extended system with an additional condition. As an example, for a finite dimensional problem, we verify the existence and local uniqueness of a double turning point numerically using the extended system and a verification method based on the Banach fixed point theorem.

Original languageEnglish
Pages (from-to)537-554
Number of pages18
JournalNumerische Mathematik
Volume97
Issue number3
DOIs
Publication statusPublished - 2004 May 1

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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