Singular integral equations of the second kind with generalized Cauchy-type kernels and variable coefficients

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8 Citations (Scopus)

Abstract

A numerical solution method is presented for singular integral equations of the second kind with a generalized Cauchy kernel and variable coefficients. The solution is constructed in the form of a product of regular and weight functions. The weight function possesses complex singularities at the ends of the interval. The parameters defining the power of these singularities are obtained by solving for the characteristic equations. A Gauss-Chebychev quadrature formula is utilized in the numerical solution of the integral equations. Benchmark examples are considered in order to illustrate the validity of the solution method.

Original languageEnglish (US)
Pages (from-to)1457-1470
Number of pages14
JournalInternational Journal for Numerical Methods in Engineering
Volume45
Issue number10
StatePublished - Aug 10 1999

Fingerprint

Singular Integral Equation
Variable Coefficients
Weight Function
Cauchy
Integral equations
Numerical Solution
Singularity
kernel
Cauchy Kernel
Gauss Quadrature
Characteristic equation
Quadrature Formula
Integral Equations
Benchmark
Interval
Form

Keywords

  • Cauchy
  • Gauss-Chebychev
  • Singular integral equations

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Applied Mathematics

Cite this

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abstract = "A numerical solution method is presented for singular integral equations of the second kind with a generalized Cauchy kernel and variable coefficients. The solution is constructed in the form of a product of regular and weight functions. The weight function possesses complex singularities at the ends of the interval. The parameters defining the power of these singularities are obtained by solving for the characteristic equations. A Gauss-Chebychev quadrature formula is utilized in the numerical solution of the integral equations. Benchmark examples are considered in order to illustrate the validity of the solution method.",
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author = "Savruk, {M. P.} and Erdogan Madenci and Shkarayev, {Sergey V}",
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AU - Savruk, M. P.

AU - Madenci, Erdogan

AU - Shkarayev, Sergey V

PY - 1999/8/10

Y1 - 1999/8/10

N2 - A numerical solution method is presented for singular integral equations of the second kind with a generalized Cauchy kernel and variable coefficients. The solution is constructed in the form of a product of regular and weight functions. The weight function possesses complex singularities at the ends of the interval. The parameters defining the power of these singularities are obtained by solving for the characteristic equations. A Gauss-Chebychev quadrature formula is utilized in the numerical solution of the integral equations. Benchmark examples are considered in order to illustrate the validity of the solution method.

AB - A numerical solution method is presented for singular integral equations of the second kind with a generalized Cauchy kernel and variable coefficients. The solution is constructed in the form of a product of regular and weight functions. The weight function possesses complex singularities at the ends of the interval. The parameters defining the power of these singularities are obtained by solving for the characteristic equations. A Gauss-Chebychev quadrature formula is utilized in the numerical solution of the integral equations. Benchmark examples are considered in order to illustrate the validity of the solution method.

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KW - Singular integral equations

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