# On the solution of the Fredholm equation of the second kind

I. G. Burova, N. S. Domnin, A. E. Vezhlev, A. V. Lebedeva, A. N. Pakulina

Research output

### 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 319-328 10 WSEAS Transactions on Mathematics 17 Published - 1 Jan 2018

### Fingerprint

Fredholm Equation
Splines
Spline
Local Polynomial
Integral equations
Integral Equations
Polynomials
Order of Approximation
Piecewise Linear
Numerical Experiment
Calculate
Experiments
Local polynomial

### 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

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title = "On the solution of the Fredholm equation of the second kind",
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.",
keywords = "Fredholm equation, Polynomial integro-differential splines, Polynomial splines",
author = "Burova, {I. G.} and Domnin, {N. S.} and Vezhlev, {A. E.} and Lebedeva, {A. V.} and Pakulina, {A. N.}",
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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

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AN - SCOPUS:85060591135

VL - 17

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EP - 328

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

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