Abstract
In the space of continuous functions, we construct Chebyshev-weight quadrature formulas exact on rational functions. On the basis of these formulas, we suggest an algorithm for the approximate solution of integral equations of the second kind. We derive accuracy estimates in terms of the best approximations to the integrands and to the kernels and right-hand sides of the integral equations by algebraic fractions with appropriate denominators.
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Original Russian Text © V.N. Rusak, I.V. Rybachenko, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 7, pp. 928–936.
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Rusak, V.N., Rybachenko, I.V. Chebyshev–Markov cosine fractions in the approximate integration and solution of integral equations. Diff Equat 51, 925–933 (2015). https://doi.org/10.1134/S0012266115070101
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DOI: https://doi.org/10.1134/S0012266115070101