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Atomic radial basis functions in numerical algorithms for solving boundary-value problems for the Laplace equation

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Abstract

A numerical method for solution of boundary-value problems of mathematical physics is described that is based on the use of radial atomic basis functions. Atomic functions are compactly supported solutions of functional-differential equations of special form. The convergence of this numerical method is investigated for the case of using an atomic function in solving the Dirichlet boundary-value problem for the Laplace equation.

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Authors and Affiliations

  1. A. N. Podgornyi Institute of Problems of Mechanical Engineering, National Academy of Sciences of Ukraine, Kharkov, Ukraine

    V. M. Kolodyazhny

  2. N. E. Zhukovskii National Aerospace University “Kharkov Aviation Institute”, Kharkov, Ukraine

    V. A. Rvachov

Authors
  1. V. M. Kolodyazhny
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  2. V. A. Rvachov
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Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 165–178, July–August 2008.

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Kolodyazhny, V.M., Rvachov, V.A. Atomic radial basis functions in numerical algorithms for solving boundary-value problems for the Laplace equation. Cybern Syst Anal 44, 603–615 (2008). https://doi.org/10.1007/s10559-008-9031-y

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  • DOI: https://doi.org/10.1007/s10559-008-9031-y

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