Identification and Discretization of the Linear Differential Equations with Constant Coefficients

In the first part of the article the problem and methods of solving the approximation and identification variational problems of the finite sequence have been stated. The method proposed is based on applying the dynamic models of the sequences under study. The peculiarities of using the models for such types of problems in the form of the ordinary linear difference equations with constant or maybe unknown coefficients have been shown here. In the second part, some problems of the discretization of the differential equations by means of the proposed problem of identification are studied. It is realized by obtaining an exact difference description of the differential equations solutions on the uniform net on the finite interval. Also, well-known analytical and proposed variational methods of the uniform discretization have been considered and compared here. With the use of the variational discretization it is not necessary to know differential coefficients. The conditions for realizing differential equations solutions on the net have been studied. Necessary and sufficient conditions for the uniqueness of the variational discretization and identification have been obtained. It is shown that under these conditions the results of the analytical and variational discretization coincide.