Numerical Quadrature of Periodic Singular Integral Equations

Steen Krenk

doi:10.1093/imamat/21.2.181

Numerical Quadrature of Periodic Singular Integral Equations

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Abstract

This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae.

Original language	English
Journal	Institute of Mathematics and Its Applications. Journal
Volume	21
Issue number	2
Pages (from-to)	181-187
ISSN	0020-2932
DOIs	https://doi.org/10.1093/imamat/21.2.181
Publication status	Published - 1978

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abstract = "This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae.",

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AB - This paper presents quadrature formulae for the numerical integration of a singular integral equation with Hilbert kernel. The formulae are based on trigonometric interpolation. By integration a quadrature formula for an integral with a logarithmic singularity is obtained. Finally it is demonstrated how a singular integral equation with infinite support can be solved by use of the preceding formulae.

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DO - 10.1093/imamat/21.2.181

M3 - Journal article

VL - 21

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EP - 187

JO - Journal of the Institute of Mathematics and Its Applications

JF - Journal of the Institute of Mathematics and Its Applications

SN - 0020-2932

IS - 2

ER -

Numerical Quadrature of Periodic Singular Integral Equations

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