This article is cited in 2 papers

Restoration of functions, integrals, and solutions to the heat conductivity equation from the Ulyanov $U_2$-classes

Y. Y. Nurmoldin

L. N. Gumilev Eurasian National University

Abstract: The paper dealt with a problem of numerical integration, and approximate restoration of functions and solutions to the heat conductivity equation with functions of distribution of starting temperatures from the classes $U_2(\beta,\theta,\alpha)$ defined by the rate of decreasing the trigonometric Fourier coefficients. Optimal orders of errors of the quadrature formulas, restoration, and discretization by the trigonometric Fourier coefficients in $L_2$ and $L_{\infty}$ metrics are obtained.

Key words: the optimal quadrature formulas, the optimal approximate restoration of functions and decisions of the heat conduction equation.

UDC: 517.5

Received: 11.04.2005
Revised: 26.05.2005

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