Numerical verification of solutions of Nekrasov's integral equation

S. Murashige*, S. Oishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 1


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

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computational Mathematics


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