TY - JOUR
T1 - Numerical verification of solutions of Nekrasov's integral equation
AU - Murashige, S.
AU - Oishi, S.
PY - 2005/7/1
Y1 - 2005/7/1
N2 - 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.
AB - 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.
KW - Nekrasov's integral equation
KW - Numerical verification
KW - Singular integral equation
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U2 - 10.1007/s00607-004-0112-0
DO - 10.1007/s00607-004-0112-0
M3 - Article
AN - SCOPUS:23744517384
SN - 0010-485X
VL - 75
SP - 15
EP - 25
JO - Computing (Vienna/New York)
JF - Computing (Vienna/New York)
IS - 1 SPEC. ISS.
ER -