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Rational interpolation and approximate solution of integral equations

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Abstract

In the space of continuous periodic functions, we construct interpolation rational operators, use them to obtain quadrature formulas with positive coefficients which are exact on rational trigonometric functions of order 2n, and suggest an algorithm for an approximate solution of integral equations of the second kind. We estimate the accuracy of the approximate solution via the best trigonometric rational approximations to the kernel and the right-hand side of the integral equation.

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Authors and Affiliations

  1. Belarus State University, Minsk, Belarus

    V. N. Rusak & N. V. Grib

  2. Belarus State Pedagogical University, Minsk, Belarus

    V. N. Rusak & N. V. Grib

Authors
  1. V. N. Rusak
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  2. N. V. Grib
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Additional information

Original Russian Text © V.N. Rusak, N.V. Grib, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 2, pp. 266–273.

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Rusak, V.N., Grib, N.V. Rational interpolation and approximate solution of integral equations. Diff Equat 48, 275–282 (2012). https://doi.org/10.1134/S0012266112020115

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  • DOI: https://doi.org/10.1134/S0012266112020115

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