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Статья
2016

Approximate solution to integral equation with logarithmic kernel of special form


I. N. MeleshkoI. N. Meleshko, P. G. LasyiP. G. Lasyi
Русская математика
https://doi.org/10.3103/S1066369X16020067
Abstract / Full Text

Based on the quadrature formula with non-negative coefficients for integral with a special logarithmic kernel, we construct and substantiate a computational pattern for solving integral equation derived from the boundary-value problem for a function, which is harmonic in the unit disk under the boundary condition of the third kind. We obtain uniform estimates of deviations of the quadrature formula and the approximate solution to integral equation.

Author information
  • Belarussian National Technical University, pr. Nezavisimosti 65, Minsk, 220013, Republic of BelarusI. N. Meleshko & P. G. Lasyi
References
  1. Kantorovich, L. V. and Krylov, V. I. Approximate Methods of Higher Analysis (Fizmatlit, Moscow–Leningrad 1962) [in Russian].
  2. Gunter, N. M. Potential Theory and its Application to Basic Problems ofMathematical Physics (GITTL, Moscow, 1953) [in Russian].
  3. Pykhteev, G. N. Approximate Computational Methods for Cauchy-Type Integrals of a Special Kind (Nauka, Novosibirsk, 1982) [in Russian].
  4. Godunov, S. K. and Ryaben’kii, V. S. Difference Schemes (Nauka, Moscow, 1977) [in Russian].