Construction and research of operators of an interlineation of functions of three variables on system of not intersected curves in a cylindrical frame with preservation of a class of differentiability

Abstract

In solving the problem of Hermite interpolation functions of three variables from its values and the values of its partial derivatives at a given point the system is not a problem of constructing operators automatically storing the class of differentiable because it completely can be solved by selecting the auxiliary functions, since the values of the function and its partial derivatives It does not affect the class of differentiable operator constructed. The mission statement is assumed that traces of derivatives of order s over the radial variable r in the cylindrical coordinate system are functions continuous together with its partial derivatives up to order v – s, 0 £ s £ N £ v £ ¥. In addition, it is believed that these derivatives are given on a system of non-intersecting lines lying on the surface of the three-dimensional body. Known R-functions method of constructing a system of coordinate functions for solving boundary value problems do not include the possibility of constructing the coordinate functions with automatic preservation of differentiability class, if the boundary function not belong to the class C^¥(G). The method of the building of the operators the hermitian type interlineations of the functions of the three variables with help of its traces and traces of its derivatives on a no crossed lines system in cylindrical coordinate system are proposed. The method can recovery these functions between given closed no crossed lines in cylindrical coordinate system with automatical preserve of a differentiability class