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

H. Kabir, Erdogan Madenci, A. Ortega

Research output: Contribution to journalArticle

28 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)617-638
Number of pages22
JournalInternational Journal for Numerical Methods in Engineering
Volume41
Issue number4
StatePublished - 1998

Fingerprint

Singular Integral Equation
Cauchy
Integral equations
Integral Equations
Logarithmic
Numerical Solution
Singularity
Cauchy-type Integral
Quadratic Polynomial
Piecewise Polynomials
Completeness
Polynomials
Numerical Results
Evaluation

Keywords

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

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Applied Mathematics

Cite this

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AU - Madenci, Erdogan

AU - Ortega, A.

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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

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