Building and research of operator approximation of functions of two variables with preservation of class Cr(R2) for traces of derivatives to a fixed order in the specified line

• Main Authors: Сергієнко, І. В., Литвин, О. М., Литвин, О. О., Ткаченко, О. В., Грицай, О. Л.
• Format: Article
• Language: Ukrainian
• Published: Journal of Mechanical Engineering 2016
• Subjects: preservation of differentiability class; function traces; the traces of the derivatives on the line; Taylor polynomial in one variable; УДК 519.6; сохранение класса дифференцируемости; следы функции; следы производных на линии; полином Тейлора по одной переменной; збереження класу диференційовності; сліди функції; сліди похідних на лінії; поліном Тейлора за однією змінною
• Online Access: https://journals.uran.ua/jme/article/view/71882

The problem of constructing a function with preservation of differentiability class has very important applications in the theory and practice of solving boundary value problems in which the boundary conditions are expressed by differential operators of the first, second and higher orders. In particular, in the solution of the biharmonic equation, if the boundary conditions are not uniform, the structural method for solving boundary value V. L. Rvachev’s problems this problem is one of the most important. If the first derivative with respect to the normal to the boundary of the region in one or more points is a continuous or once differentiable function of one variable, the existing methods for constructing structures of boundary value problems will be automatically carry these qualities into the domain of integration. At the same time the classical methods of solving boundary value problems continue to monitor the solution inside the domain while preserving infinitely differentiable. In this article construction and research of an operator of approach of functions of 2 variables with preservation of a class Cr(R2) with help these tracks and tracks these derivations of the fixed order on given curve. Development of the methods of the recovery of the functions of two variables with preservation of the class Cr(R2) in the neighborhood curve of the class Cr. The methods using the tracks the functions and tracks these derivations until of the fixed order on given curve