Numerical verification of existence and inclusion of solutions for nonlinear operator equations

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    10 Citations (Scopus)

    Abstract

    Nonlinear operator equations of the type f(u) ≡ Lu + Nu = 0, u ∈ D(L) are considered, where L is a closed linear operator from a Banach space X to another Banach space Y and N a nonlinear operator from X to Y. A method is presented for numerical verification and inclusion of solutions for the equations. As an example, the existence of a periodic solution is proved for the Duffing equation.

    Original languageEnglish
    Pages (from-to)171-185
    Number of pages15
    JournalJournal of Computational and Applied Mathematics
    Volume60
    Issue number1-2
    DOIs
    Publication statusPublished - 1995 Jun 20

    Fingerprint

    Numerical Verification
    Nonlinear Operator Equations
    Banach spaces
    Mathematical operators
    Inclusion
    Banach space
    Duffing Equation
    Closed Operator
    Nonlinear Operator
    Linear Operator
    Periodic Solution

    Keywords

    • Computer-assisted existence proof
    • Duffing's equation
    • Newton's method
    • Self-validating numerics
    • Urabe-Galerkin's method

    ASJC Scopus subject areas

    • Applied Mathematics
    • Computational Mathematics

    Cite this

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    abstract = "Nonlinear operator equations of the type f(u) ≡ Lu + Nu = 0, u ∈ D(L) are considered, where L is a closed linear operator from a Banach space X to another Banach space Y and N a nonlinear operator from X to Y. A method is presented for numerical verification and inclusion of solutions for the equations. As an example, the existence of a periodic solution is proved for the Duffing equation.",
    keywords = "Computer-assisted existence proof, Duffing's equation, Newton's method, Self-validating numerics, Urabe-Galerkin's method",
    author = "Shinichi Oishi",
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    KW - Self-validating numerics

    KW - Urabe-Galerkin's method

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