Systems of functions orthogonal in the sense of Sobolev associated with Haar functions and the Cauchy problem for ODEs

I. I. Sharapudinov ; S. R. Magomedov

Daghestan Electronic Mathematical Reports, Tome 7 (2017), pp. 1-15.

Résumé

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 $$. 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).

Détail

Keywords: systems of functions orthogonal in the sense of Sobolev, Haar functions, the Cauchy problem for an ODE.

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