### 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 language | English (US) |
---|---|

Pages (from-to) | 1457-1470 |

Number of pages | 14 |

Journal | International Journal for Numerical Methods in Engineering |

Volume | 45 |

Issue number | 10 |

State | Published - Aug 10 1999 |

### Fingerprint

### Keywords

- Cauchy
- Gauss-Chebychev
- Singular integral equations

### ASJC Scopus subject areas

- Engineering (miscellaneous)
- Computational Mechanics
- Applied Mathematics

### Cite this

**Singular integral equations of the second kind with generalized Cauchy-type kernels and variable coefficients.** / Savruk, M. P.; Madenci, Erdogan; Shkarayev, Sergey V.

Research output: Contribution to journal › Article

*International Journal for Numerical Methods in Engineering*, vol. 45, no. 10, pp. 1457-1470.

}

TY - JOUR

T1 - Singular integral equations of the second kind with generalized Cauchy-type kernels and variable coefficients

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.

KW - Cauchy

KW - Gauss-Chebychev

KW - Singular integral equations

UR - http://www.scopus.com/inward/record.url?scp=0040220124&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040220124&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040220124

VL - 45

SP - 1457

EP - 1470

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 10

ER -