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Approximate collocation method for an integral equation with a logarithmic kernel

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Abstract

An integral operator is defined on the set of functions expandable in a Fourier-Chebyshev series. The expansion is used to prove convergence of the proposed method and an error bound is derived.Consider the integral operator L,

$$L\varphi = \frac{1}{\pi }\int\limits_{ - 1}^1 {\ln \left| {x - t} \right|\frac{{\varphi (t)}}{{\sqrt {1 - t^2 } }}dt} ,\left| x \right| \leqslant 1.$$
((1))

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References

  1. A. S. Il'inskii and Yu. G. Smirnov, “Investigation of mathematical models of microstrip lines,” in: Methods of Mathematical Modeling, Computer-Aided Processing of Observations, and Their Applications [in Russian], Izd. MGU, Moscow (1986), pp. 176–198.

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  2. P. K. Suetin, Classical Orthogonal Polynomials [in Russian], Nauka, Moscow (1976).

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  3. S. M. Nikol'skii, Quadrature Formulas [in Russian], Nauka, Moscow (1974).

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Authors
  1. A. S. Il'inskii
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Additional information

Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 28–32.

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Il'inskii, A.S. Approximate collocation method for an integral equation with a logarithmic kernel. Comput Math Model 8, 106–111 (1997). https://doi.org/10.1007/BF02405159

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  • DOI: https://doi.org/10.1007/BF02405159

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