оператор Стеклова

The Solution of a Certain Inverse Problem

Authors: Khromov A. A.

The solution is given for the problem of findinging uniform approximations of a the right-hand side of a general linear ordinary differential equation in the case when approximations of the exact solution are known. The constructed method has a simple structure, produces approximations of the right-hand side on the whole interval of definition and does not employ boundary conditions.

The Solution of the Problem of Determining the Density of Heat Sources in a Rod

Authors: Khromov A. A., Khromova G. V.

We give a solution of a problem of determining the density of heat sources in the bav, which is set to a fixed temperature, if the temperature is given approximately. Mathematically it is the problem of finding uniform approximations to the right-hand side of the ordinary differential equation when uniform approximations to the solution and values of error are known.

Regularization of Abel Equation with the Use of Discontinuous Steklov Operator

Authors: Khromova G. V.

For getting uniform approximations of the exact solution of Abel equation with an approximate right-hand part a simply constructed family of integral operators is suggested.

Approximation of Function and Its Derivative by the Modificated Steklov Operator

Authors: Khromov A. A.

With the use of modification of Steklov operator are constructed families of integral operator which allow us to get uniform derivative on a closed.