### Abstract

- The present paper is devoted to the application of local polynomial integro-differential splines to the solution of integral equations, in particular, to the solution of the integral equations of Fredholm of the second kind. To solve the Fredholm equation of the second kind, we apply local polynomial integro-differential splines of the second and third order of approximation. To calculate the integral in the formulae of a piecewise quadratic integro-differential spline and piecewise linear integro-differential spline, we propose the corresponding quadrature formula. The results of the numerical experiments are given.

Original language | English |
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Pages (from-to) | 319-328 |

Number of pages | 10 |

Journal | WSEAS Transactions on Mathematics |

Volume | 17 |

Publication status | Published - 1 Jan 2018 |

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### Scopus subject areas

- Algebra and Number Theory
- Endocrinology, Diabetes and Metabolism
- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Management Science and Operations Research
- Control and Optimization
- Computational Mathematics
- Applied Mathematics

### Cite this

*WSEAS Transactions on Mathematics*,

*17*, 319-328.

}

*WSEAS Transactions on Mathematics*, vol. 17, pp. 319-328.

**On the solution of the Fredholm equation of the second kind.** / Burova, I. G.; Domnin, N. S.; Vezhlev, A. E.; Lebedeva, A. V.; Pakulina, A. N.

Research output

TY - JOUR

T1 - On the solution of the Fredholm equation of the second kind

AU - Burova, I. G.

AU - Domnin, N. S.

AU - Vezhlev, A. E.

AU - Lebedeva, A. V.

AU - Pakulina, A. N.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - - The present paper is devoted to the application of local polynomial integro-differential splines to the solution of integral equations, in particular, to the solution of the integral equations of Fredholm of the second kind. To solve the Fredholm equation of the second kind, we apply local polynomial integro-differential splines of the second and third order of approximation. To calculate the integral in the formulae of a piecewise quadratic integro-differential spline and piecewise linear integro-differential spline, we propose the corresponding quadrature formula. The results of the numerical experiments are given.

AB - - The present paper is devoted to the application of local polynomial integro-differential splines to the solution of integral equations, in particular, to the solution of the integral equations of Fredholm of the second kind. To solve the Fredholm equation of the second kind, we apply local polynomial integro-differential splines of the second and third order of approximation. To calculate the integral in the formulae of a piecewise quadratic integro-differential spline and piecewise linear integro-differential spline, we propose the corresponding quadrature formula. The results of the numerical experiments are given.

KW - Fredholm equation

KW - Polynomial integro-differential splines

KW - Polynomial splines

UR - http://www.scopus.com/inward/record.url?scp=85060591135&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85060591135

VL - 17

SP - 319

EP - 328

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

ER -