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Optimal by the order methods of solving integral equations in a special case

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Abstract

We study an integral equation of the third kind with fixed singularities of the kernel. We suggest and substantiate special generalized versions of spline methods for approximate solving these equations in the space of distributions. We show that the constructed methods are optimal by the order.

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Authors and Affiliations

  1. Naberezhnye Chelny Institute of Kazan Federal University, pr. Mira 68/19, Naberezhnye Chelny, 423810, Russia

    N. S. Gabbasov

  2. Naberezhnye Chelny Branch of Kazan Innovation University, pr. Vakhitova 53/02, Naberezhnye Chelny, 423815, Russia

    Z. Kh. Galimova

Authors
  1. N. S. Gabbasov
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  2. Z. Kh. Galimova
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Correspondence to N. S. Gabbasov.

Additional information

Original Russian Text © N.S. Gabbasov, Z.Kh. Galimova, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 9, pp. 3–12.

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Gabbasov, N.S., Galimova, Z.K. Optimal by the order methods of solving integral equations in a special case. Russ Math. 61, 1–9 (2017). https://doi.org/10.3103/S1066369X17090018

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  • DOI: https://doi.org/10.3103/S1066369X17090018

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