Numerische Mathematik

, Volume 97, Issue 3, pp 537–554

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

  • Ken’ichiro Tanaka
  • Sunao Murashige
  • Shin’ichi Oishi

DOI: 10.1007/s00211-003-0515-4

Cite this article as:
Tanaka, K., Murashige, S. & Oishi, S. Numer. Math. (2004) 97: 537. doi:10.1007/s00211-003-0515-4


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ken’ichiro Tanaka
    • 1
  • Sunao Murashige
    • 2
  • Shin’ichi Oishi
    • 3
  1. 1.Department of Mathematical InformaticsGraduate School of Information Science and TechnologyJapan
  2. 2.Department of Complexity Science and EngineeringGraduate School of Frontier SciencesJapan
  3. 3.Department of Computer ScienceSchool of Science and EngineeringTokyoJapan