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This article is cited in 7 scientific papers (total in 7 papers)
Approximation of the solution of the Cauchy problem for nonlinear ODE systems by means of Fourier series in functions orthogonal in the sense of Sobolev
I. I. Sharapudinovab a Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
b Vladikavkaz Scientific Centre of the Russian Academy of Sciences
Abstract:
Consider the systems of functions ${\varphi}_{r,n}(x)$ $(r=1,2,\ldots, n=0,1,\ldots)$ orthonormal with respect to a Sobolev-type inner product of the form $\langle f,g\rangle= \sum_{\nu=0}^{r-1}f^{(\nu)}(a)g^{(\nu)}(a)+\int_{a}^{b}f^{(r)}(x)g^{(r)}\rho(x)(x)dx$ generated by a given orthonormal system of functions ${\varphi}_{n}(x)$ $( n=0,1,\ldots)$. It is shown that the Fourier series in the system ${\varphi}_{r,n}(x)$ $(r=1,2,\ldots, n=0,1,\ldots)$ and their partial sums are a convenient and very effective tool for the approximate solution of the Cauchy problem for ordinary differential equations (ODEs).
Keywords:
the Cauchy problem, Fourier series, Sobolev orthogonal functions.
Received: 31.03.2017 Revised: 18.05.2017 Accepted: 19.05.2017
Citation:
I. I. Sharapudinov, “Approximation of the solution of the Cauchy problem for nonlinear ODE systems by means of Fourier series in functions orthogonal in the sense of Sobolev”, Daghestan Electronic Mathematical Reports, 2017, no. 7, 66–76
Linking options:
https://www.mathnet.ru/eng/demr39 https://www.mathnet.ru/eng/demr/y2017/i7/p66
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