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This article is cited in 4 scientific papers (total in 4 papers)
Systems of functions orthogonal in the sense of Sobolev associated with Haar functions and the Cauchy problem for ODEs
I. I. Sharapudinovab, S. R. Magomedova a Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
b Vladikavkaz Scientific Centre of the Russian Academy of Sciences
Abstract:
We consider systems of functions ${\mathcal{X}}_{r,n}(x)$ $(r=1,2,\ldots, n=0,1,\ldots)$, generated by Haar functions $\chi_{n}(x)$ $(n=1,2,\ldots)$, that form the Sobolev orthonormal system with respect to the scalar product of the following form $<f,g>=\sum_{\nu=0}^{r-1}f^{(\nu)}(0)g^{(\nu)}(0)+\int_{0}^{1}f^{(r)}(t)g^{(r)}(x)dx$. It is shown that the Fourier series and sums with respect to the system ${\mathcal{X}}_{r,n}(x)$ $(n=0,1,\ldots)$ are a convenient and very effective tool for the approximate solution of the Cauchy problem for ordinary differential equations (ODEs).
Keywords:
systems of functions orthogonal in the sense of Sobolev, Haar functions, the Cauchy problem for an ODE.
Received: 06.03.2017 Revised: 10.04.2017 Accepted: 12.04.2017
Citation:
I. I. Sharapudinov, S. R. Magomedov, “Systems of functions orthogonal in the sense of Sobolev associated with Haar functions and the Cauchy problem for ODEs”, Daghestan Electronic Mathematical Reports, 2017, no. 7, 1–15
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https://www.mathnet.ru/eng/demr32 https://www.mathnet.ru/eng/demr/y2017/i7/p1
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