|
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 $\Omega_N=\left\{ 0,1,\ldots,N-1 \right\}$ system of functions ${\psi}_{n}(x,N)$ $( n=0,1,\ldots,N-1)$.
These new functions are orthonormal with respect to the inner product of the following type: $\langle f,g\rangle = f(0)g(0)+
\sum_{j=0}^{N-1}\Delta f(j)\Delta g(j)\rho(j)$.
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.
Received: 07.04.2017 Revised: 17.04.2017 Accepted: 18.04.2017
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
Linking options:
https://www.mathnet.ru/eng/demr40 https://www.mathnet.ru/eng/demr/y2017/i7/p77
|
Statistics & downloads: |
Abstract page: | 141 | Full-text PDF : | 26 | References: | 15 |
|