Numerical verification of solutions of Nekrasov's integral equation

S. Murashige, Shinichi Oishi

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    This paper describes numerical verification of solutions of Nekrasov's integral equation which is a mathematical model of two-dimensional water waves. This nonlinear and periodic integral equation includes a logarithmic singular kernel which is typically found in some two-dimensional potential problems. We propose the verification method using some properties of the singular integral for trigonometric polynomials and Schauder's fixed point theorem in the periodic Sobolev space. A numerical example shows effectiveness of the present method.

    Original languageEnglish
    Pages (from-to)15-25
    Number of pages11
    JournalComputing (Vienna/New York)
    Volume75
    Issue number1 SPEC. ISS.
    DOIs
    Publication statusPublished - 2005 Jul

    Fingerprint

    Numerical Verification
    Integral equations
    Integral Equations
    Logarithmic Kernel
    Singular Kernel
    Sobolev spaces
    Schauder Fixed Point Theorem
    Potential Problems
    Trigonometric Polynomial
    Singular Integrals
    Water waves
    Water Waves
    Sobolev Spaces
    Polynomials
    Mathematical Model
    Mathematical models
    Numerical Examples

    Keywords

    • Nekrasov's integral equation
    • Numerical verification
    • Singular integral equation

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics

    Cite this

    Numerical verification of solutions of Nekrasov's integral equation. / Murashige, S.; Oishi, Shinichi.

    In: Computing (Vienna/New York), Vol. 75, No. 1 SPEC. ISS., 07.2005, p. 15-25.

    Research output: Contribution to journalArticle

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