Numerical verification of solutions of Nekrasov's integral equation

S. Murashige, Shinichi Oishi

    Research output: Contribution to journalArticle

    2 Citations (Scopus)


    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)
    Issue number1 SPEC. ISS.
    Publication statusPublished - 2005 Jul



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

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Theory and Mathematics

    Cite this