Numerical solution of integral equations with logarithmic-, cauchy- and hadamard-type singularities

H. Kabir; E. Madenci; A. Ortega

doi:10.1002/(SICI)1097-0207(19980228)41:4<617::AID-NME301>3.0.CO;2-K

Numerical solution of integral equations with logarithmic-, cauchy- and hadamard-type singularities

H. Kabir
, E. Madenci
, A. Ortega

Aerospace and Mechanical Engineering

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

31 Scopus citations

Abstract

This study presents an extension of the piecewise quadratic polynomial technique to solve singular integral equations with logarithmic- and Hadamard-type singularities. For completeness and continuity, the evaluation of the weights for logarithmic-, Cauchy- and Hadamard-type singularities are given explicitly. Numerical results concerning logarithmic- and Hadamard-type singular integral equations are compared with the known solutions. The solution of Cauchy-type singular integral equations was discussed in detail in a previous study by Miller and Keer.¹⁸

Original language	English (US)
Pages (from-to)	617-638
Number of pages	22
Journal	International Journal for Numerical Methods in Engineering
Volume	41
Issue number	4
DOIs	https://doi.org/10.1002/(SICI)1097-0207(19980228)41:4<617::AID-NME301>3.0.CO;2-K
State	Published - 1998

Keywords

Logarithmic-, Cauchy- and hadamard-type singularities
Singular integral equations

ASJC Scopus subject areas

Numerical Analysis
General Engineering
Applied Mathematics

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10.1002/(SICI)1097-0207(19980228)41:4<617::AID-NME301>3.0.CO;2-K

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title = "Numerical solution of integral equations with logarithmic-, cauchy- and hadamard-type singularities",

abstract = "This study presents an extension of the piecewise quadratic polynomial technique to solve singular integral equations with logarithmic- and Hadamard-type singularities. For completeness and continuity, the evaluation of the weights for logarithmic-, Cauchy- and Hadamard-type singularities are given explicitly. Numerical results concerning logarithmic- and Hadamard-type singular integral equations are compared with the known solutions. The solution of Cauchy-type singular integral equations was discussed in detail in a previous study by Miller and Keer.18",

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author = "H. Kabir and E. Madenci and A. Ortega",

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T1 - Numerical solution of integral equations with logarithmic-, cauchy- and hadamard-type singularities

AU - Kabir, H.

AU - Madenci, E.

AU - Ortega, A.

PY - 1998

Y1 - 1998

N2 - This study presents an extension of the piecewise quadratic polynomial technique to solve singular integral equations with logarithmic- and Hadamard-type singularities. For completeness and continuity, the evaluation of the weights for logarithmic-, Cauchy- and Hadamard-type singularities are given explicitly. Numerical results concerning logarithmic- and Hadamard-type singular integral equations are compared with the known solutions. The solution of Cauchy-type singular integral equations was discussed in detail in a previous study by Miller and Keer.18

AB - This study presents an extension of the piecewise quadratic polynomial technique to solve singular integral equations with logarithmic- and Hadamard-type singularities. For completeness and continuity, the evaluation of the weights for logarithmic-, Cauchy- and Hadamard-type singularities are given explicitly. Numerical results concerning logarithmic- and Hadamard-type singular integral equations are compared with the known solutions. The solution of Cauchy-type singular integral equations was discussed in detail in a previous study by Miller and Keer.18

KW - Logarithmic-, Cauchy- and hadamard-type singularities

KW - Singular integral equations

UR - https://www.scopus.com/pages/publications/0032002438

UR - https://www.scopus.com/pages/publications/0032002438#tab=citedBy

U2 - 10.1002/(SICI)1097-0207(19980228)41:4<617::AID-NME301>3.0.CO;2-K

DO - 10.1002/(SICI)1097-0207(19980228)41:4<617::AID-NME301>3.0.CO;2-K

M3 - Article

AN - SCOPUS:0032002438

SN - 0029-5981

VL - 41

SP - 617

EP - 638

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

IS - 4

ER -

Numerical solution of integral equations with logarithmic-, cauchy- and hadamard-type singularities

Abstract

Keywords

ASJC Scopus subject areas

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