Numerical verification of solutions of periodic integral equations with a singular kernel

Sunao Murashige, Shinichi Oishi

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    This paper proposes the method of numerical verification of solutions of a periodic integral equation with a logarithmic singular kernel, which is typically found in some two-dimensional potential problems. The verification method utilizes a property of the singular integral for trigonometric polynomials, the periodic Sobolev space and Schauder's fixed point theorem.

    Original languageEnglish
    Pages (from-to)301-310
    Number of pages10
    JournalNumerical Algorithms
    Volume37
    Issue number1-4 SPEC. ISS.
    DOIs
    Publication statusPublished - 2004 Dec

    Fingerprint

    Singular Kernel
    Numerical Verification
    Integral equations
    Integral Equations
    Logarithmic Kernel
    Sobolev spaces
    Schauder Fixed Point Theorem
    Potential Problems
    Trigonometric Polynomial
    Singular Integrals
    Sobolev Spaces
    Polynomials

    Keywords

    • numerical verification
    • potential problem
    • singular integral equation

    ASJC Scopus subject areas

    • Applied Mathematics

    Cite this

    Numerical verification of solutions of periodic integral equations with a singular kernel. / Murashige, Sunao; Oishi, Shinichi.

    In: Numerical Algorithms, Vol. 37, No. 1-4 SPEC. ISS., 12.2004, p. 301-310.

    Research output: Contribution to journalArticle

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