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Daghestan Electronic Mathematical Reports, 2017, Issue 7, Pages 29–39 (Mi demr34)  

This article is cited in 1 scientific paper (total in 1 paper)

Sobolev orthogonal functions on the grid, generated by discrete orthogonal functions and the Cauchy problem for the difference equation

I. I. Sharapudinovab, Z. D. Gadzhievaac, R. M. Gadzhimirzaeva

a Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
b Vladikavkaz Scientific Centre of the Russian Academy of Sciences
c Daghestan State Pedagogical University

Abstract: We consider the system of functions ${\psi}_{r,n}(x)$ $(r=1,2,\ldots, n=0,1,\ldots)$ orthonormal on Sobolev with respect to the inner product of the form $\langle f,g\rangle=\sum_{k=0}^{r-1}\Delta^kf(0)\Delta^kg(0)+ \sum_{j=0}^\infty\Delta^rf(j)\Delta^rg(j)\rho(j)$, generated by a given orthonormal system of functions ${\psi}_{n}(x)$ $( n=0,1,\ldots)$. It is shown that the Fourier series and Fourier sums by the system ${\psi}_{r,n}(x)$ $(r = 1,2, \ldots, n = 0,1, \ldots)$ are convenient and a very effective tool for the approximate solution of the Cauchy problem for difference equations.

Keywords: Sobolev orthogonal functions, functions orthogonal on the grid, approximation of discrete functions, mixed series by the functions ortho-\linebreak gonal on a uniform grid, iterative process for the approximate solution of difference equations

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00486a
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00486a)


DOI: https://doi.org/10.31029/demr.7.3

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UDC: 517.912
Received: 07.04.2017
Revised: 26.04.2017
Accepted:27.04.2017
Language:

Citation: I. I. Sharapudinov, Z. D. Gadzhieva, R. M. Gadzhimirzaev, “Sobolev orthogonal functions on the grid, generated by discrete orthogonal functions and the Cauchy problem for the difference equation”, Daghestan Electronic Mathematical Reports, 2017, no. 7, 29–39

Citation in format AMSBIB
\Bibitem{ShaGadGad17}
\by I.~I.~Sharapudinov, Z.~D.~Gadzhieva, R.~M.~Gadzhimirzaev
\paper Sobolev orthogonal functions on the grid, generated by discrete orthogonal functions and the Cauchy problem for the difference equation
\jour Daghestan Electronic Mathematical Reports
\yr 2017
\issue 7
\pages 29--39
\mathnet{http://mi.mathnet.ru/demr34}
\crossref{https://doi.org/10.31029/demr.7.3}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. S. Sultanakhmedov, “Cauchy problem for the difference equation and Sobolev orthogonal functions on the finite grid, generated by discrete orthogonal functions”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 7, 77–85  mathnet  crossref
  • Daghestan Electronic Mathematical Reports
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