Construction and research of operators of a Hermite interlineation of functions two variables on system of not intersected lines with preservation of differential class

Abstract

Investigates methods for constructing Hermitian operators interlination recovery of differentiated functions of two variables between the smooth continuous curves that preserve the class of differentiability C^r(R²). To construct these operators are used traces of the interpolated function and its partial derivatives with respect to one variable to a given order. The method of constructing these operators are based on the method first proposed in O. N. Lytvyn and uses a linear combination of the integral operators, allowing to increase the relevant classes of differentiable functions that are built with the following, which are assumed not to have the required class of differentiability. Thus said linear combination belongs to a specific class of differentiability despite the value of the linear combination coefficients. These values are found from the condition that corresponding derivatives of the variable y have the same traces as the approximated function on all M non-intersecting curves. Thus constructed operators retain the same differentiability class r, which owns the approximated function f(x, y) and at the same has the same traces as the approximated function with partial derivatives y with respect to the order N inclusive. In this paper, accepted that the functions describing these curves have continuous derivatives to order r including and those curves do not intersect.