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

Ken'ichiro Tanaka, Sunao Murashige, Shinichi Oishi

    Research output: Contribution to journalArticle

    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

    Fingerprint

    Numerical Verification
    Extended Systems
    Turning Point
    Necessary Conditions
    Sufficient Conditions
    Verify
    Banach Fixed Point Theorem
    Nonlinear systems
    Uniqueness
    Nonlinear Systems

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics
    • Computational Mathematics

    Cite this

    On necessary and sufficient conditions for numerical verification of double turning points. / Tanaka, Ken'ichiro; Murashige, Sunao; Oishi, Shinichi.

    In: Numerische Mathematik, Vol. 97, No. 3, 05.2004, p. 537-554.

    Research output: Contribution to journalArticle

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