Numerical verification of solutions of periodic integral equations with a singular kernel

Sunao Murashige; Shin'ichi Oishi

doi:10.1023/B:NUMA.0000049476.37729.99

Numerical verification of solutions of periodic integral equations with a singular kernel

Sunao Murashige, Shin'ichi Oishi

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

This paper proposes the method of numerical verification of solutions of a periodic integral equation with a logarithmic singular kernel, which is typically found in some two-dimensional potential problems. The verification method utilizes a property of the singular integral for trigonometric polynomials, the periodic Sobolev space and Schauder's fixed point theorem.

Original language	English
Pages (from-to)	301-310
Number of pages	10
Journal	Numerical Algorithms
Volume	37
Issue number	1-4 SPEC. ISS.
DOIs	https://doi.org/10.1023/B:NUMA.0000049476.37729.99
Publication status	Published - 2004 Dec

Keywords

numerical verification
potential problem
singular integral equation

ASJC Scopus subject areas

Applied Mathematics

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10.1023/B:NUMA.0000049476.37729.99

Cite this

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title = "Numerical verification of solutions of periodic integral equations with a singular kernel",

abstract = "This paper proposes the method of numerical verification of solutions of a periodic integral equation with a logarithmic singular kernel, which is typically found in some two-dimensional potential problems. The verification method utilizes a property of the singular integral for trigonometric polynomials, the periodic Sobolev space and Schauder's fixed point theorem.",

keywords = "numerical verification, potential problem, singular integral equation",

author = "Sunao Murashige and Shin'ichi Oishi",

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AB - This paper proposes the method of numerical verification of solutions of a periodic integral equation with a logarithmic singular kernel, which is typically found in some two-dimensional potential problems. The verification method utilizes a property of the singular integral for trigonometric polynomials, the periodic Sobolev space and Schauder's fixed point theorem.

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Numerical verification of solutions of periodic integral equations with a singular kernel

Abstract

Keywords

ASJC Scopus subject areas

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