Imperfect singular solutions of nonlinear equations and a numerical method of proving their existence

Yuchi Kanzawa, Shinichi Oishi

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    A new concept of "an imperfect singular solution" is defined as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations. A numerical method is presented for proving the existence of imperfect singular solutions of nonlinear equations with guaranteed accuracy. A few numerical examples are also presented for illustration.

    Original languageEnglish
    Pages (from-to)1062-1069
    Number of pages8
    JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
    VolumeE82-A
    Issue number6
    Publication statusPublished - 1999

    Fingerprint

    Singular Solutions
    Nonlinear equations
    Imperfect
    Numerical methods
    Nonlinear Equations
    Numerical Methods
    Small Perturbations
    Approximate Solution
    Numerical Examples

    Keywords

    • Imperfect singular solutions extended systems
    • Krawczyk-based interval validation method
    • Numerical computation with guaranteed accuracy

    ASJC Scopus subject areas

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

    Cite this

    @article{367f2d05ffa7428486e65bb6c537448b,
    title = "Imperfect singular solutions of nonlinear equations and a numerical method of proving their existence",
    abstract = "A new concept of {"}an imperfect singular solution{"} is defined as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations. A numerical method is presented for proving the existence of imperfect singular solutions of nonlinear equations with guaranteed accuracy. A few numerical examples are also presented for illustration.",
    keywords = "Imperfect singular solutions extended systems, Krawczyk-based interval validation method, Numerical computation with guaranteed accuracy",
    author = "Yuchi Kanzawa and Shinichi Oishi",
    year = "1999",
    language = "English",
    volume = "E82-A",
    pages = "1062--1069",
    journal = "IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences",
    issn = "0916-8508",
    publisher = "Maruzen Co., Ltd/Maruzen Kabushikikaisha",
    number = "6",

    }

    TY - JOUR

    T1 - Imperfect singular solutions of nonlinear equations and a numerical method of proving their existence

    AU - Kanzawa, Yuchi

    AU - Oishi, Shinichi

    PY - 1999

    Y1 - 1999

    N2 - A new concept of "an imperfect singular solution" is defined as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations. A numerical method is presented for proving the existence of imperfect singular solutions of nonlinear equations with guaranteed accuracy. A few numerical examples are also presented for illustration.

    AB - A new concept of "an imperfect singular solution" is defined as an approximate solution which becomes a singular solution by adding a suitable small perturbation to the original equations. A numerical method is presented for proving the existence of imperfect singular solutions of nonlinear equations with guaranteed accuracy. A few numerical examples are also presented for illustration.

    KW - Imperfect singular solutions extended systems

    KW - Krawczyk-based interval validation method

    KW - Numerical computation with guaranteed accuracy

    UR - http://www.scopus.com/inward/record.url?scp=0032684913&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0032684913&partnerID=8YFLogxK

    M3 - Article

    AN - SCOPUS:0032684913

    VL - E82-A

    SP - 1062

    EP - 1069

    JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

    JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

    SN - 0916-8508

    IS - 6

    ER -