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 language | English |
|---|---|
| Pages (from-to) | 15-25 |
| Number of pages | 11 |
| Journal | Computing (Vienna/New York) |
| Volume | 75 |
| Issue number | 1 SPEC. ISS. |
| DOIs | |
| Publication status | Published - 2005 Jul 1 |
Keywords
- 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