Atomic radial basis functions in numerical algorithms for solving boundary-value problems for the Laplace equation |
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| Authors: | V. M. Kolodyazhny V. A. Rvachov |
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| Affiliation: | (1) A. N. Podgornyi Institute of Problems of Mechanical Engineering, National Academy of Sciences of Ukraine, Kharkov, Ukraine;(2) N. E. Zhukovskii National Aerospace University “Kharkov Aviation Institute”, Kharkov, Ukraine |
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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. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 165–178, July–August 2008. |
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| Keywords: | atomic function functional-differential equation harmonic function radial basis function approximation error |
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