A method of proving the existence of simple turning points of two-point boundary value problems based on the numerical computation with guaranteed accuracy

Takao Soma, Shinichi Oishi, Yuchi Kanzawa, Kazuo Horiuchi

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    This paper is concerned with the validation of simple turning points of two-point boundary value problems of nonlinear ordinary differential equations. Usually it is hard to validate approximate solutions of turning points numerically because of it's singularity. In this paper, it is pointed out that applying the infinite dimensional Krawcyzk-based interval validation method to enlarged system, the existence of simple turning points can be verified. Taking an example, the result of validation is also presented.

    Original languageEnglish
    Pages (from-to)1892-1897
    Number of pages6
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    VolumeE81-A
    Issue number9
    Publication statusPublished - 1998

    Fingerprint

    Turning Point
    Two-point Boundary Value Problem
    Numerical Computation
    Boundary value problems
    Nonlinear Ordinary Differential Equations
    Ordinary differential equations
    Approximate Solution
    Singularity
    Interval

    Keywords

    • Enlarged systems
    • Krawczyk's mapping
    • Numerical computation with guaranteed accuracy
    • Turning points
    • Two-point boundary-value problems

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Hardware and Architecture
    • Information Systems

    Cite this

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    abstract = "This paper is concerned with the validation of simple turning points of two-point boundary value problems of nonlinear ordinary differential equations. Usually it is hard to validate approximate solutions of turning points numerically because of it's singularity. In this paper, it is pointed out that applying the infinite dimensional Krawcyzk-based interval validation method to enlarged system, the existence of simple turning points can be verified. Taking an example, the result of validation is also presented.",
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    AU - Oishi, Shinichi

    AU - Kanzawa, Yuchi

    AU - Horiuchi, Kazuo

    PY - 1998

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    AB - This paper is concerned with the validation of simple turning points of two-point boundary value problems of nonlinear ordinary differential equations. Usually it is hard to validate approximate solutions of turning points numerically because of it's singularity. In this paper, it is pointed out that applying the infinite dimensional Krawcyzk-based interval validation method to enlarged system, the existence of simple turning points can be verified. Taking an example, the result of validation is also presented.

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