
Daghestan Electronic Mathematical Reports, 2017, Issue 7, Pages 77–85
(Mi demr40)




This article is cited in 1 scientific paper (total in 1 paper)
Cauchy problem for the difference equation and Sobolev orthogonal functions on the finite grid, generated by discrete orthogonal functions
M. S. Sultanakhmedov^{} ^{} Daghestan scientific center of RAS
Abstract:
We consider the system of functions ${\psi}_{1,n}(x, N)$ ($n=0,1,\ldots,$ $N$), orthonormal in Sobolev sense and generated by a given orthonormal on finite grid $\Omega_N=\{ 0,1,\ldots,N1 \}$ system of functions ${\psi}_{n}(x,N)$ $( n=0,1,\ldots,N1)$.
These new functions are orthonormal with respect to the inner product of the following type: $\langle f,g\rangle = f(0)g(0)+
\sum_{j=0}^{N1}\Delta f(j)\Delta g(j)\rho(j)$.
It is shown that the finite Fourier series by the functions
${\psi}_{1,n}(x)$ and their partial sums are convenient and a very effective tool for the approximate solution of the Cauchy problem for nonlinear difference equations.
Keywords:
Sobolev orthogonal functions; functions orthogonal on the finite grid; finite grid; uniform grid; approximation of discrete functions; mixed series by the functions orthogonal on a uniform grid; iterative process for the approximate solution of difference equations
DOI:
https://doi.org/10.31029/demr.7.9
Full text:
PDF file (349 kB)
Full text:
http://mathreports.ru/.../cauchyproblemforthedifferenceequationandsobolevorthogonalfunctionsonthefinitegridgener
References:
PDF file
HTML file
UDC:
517.912 Received: 07.04.2017 Revised: 17.04.2017 Accepted:18.04.2017
Language:
Citation:
M. S. Sultanakhmedov, “Cauchy problem for the difference equation and Sobolev orthogonal functions on the finite grid, generated by discrete orthogonal functions”, Daghestan Electronic Mathematical Reports, 2017, no. 7, 77–85
Citation in format AMSBIB
\Bibitem{Sul17}
\by M.~S.~Sultanakhmedov
\paper Cauchy problem for the difference equation and Sobolev orthogonal functions on the finite grid, generated by discrete orthogonal functions
\jour Daghestan Electronic Mathematical Reports
\yr 2017
\issue 7
\pages 7785
\mathnet{http://mi.mathnet.ru/demr40}
\crossref{https://doi.org/10.31029/demr.7.9}
Linking options:
http://mi.mathnet.ru/eng/demr40 http://mi.mathnet.ru/eng/demr/y2017/i7/p77
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:

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”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 7, 29–39

Number of views: 
This page:  32  Full text:  6  References:  6 
