Numerical solution to the initial-final problem for non-stationary Leontief-type systems

M. A. Sagadeeva   ; L. M. Fatkulllina   ; O. V. Ufimtseva

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 13 (2021) no. 2, pp. 30-36

Résumé

The main purpose of the paper is to prove the convergence of a numerical solution to a non-stationary Leontief-type system with an initial-final condition. Non-stationary Leontief-type systems are used in the study of dynamic balance models of the economy. Nonstationarity of systems is described using a scalar function, which is multiplied by one of the matrices of the system. The distinctive feature of Leontief-type systems is the matrix singularity at the derivative with time, which is due to the fact that some types of resources of economic systems cannot be stored. In the article, the initial-final condition is used instead of the standard initial condition, which for economic systems can be interpreted as taking into account indicators not only at the initial moment of time, but also indicators that will be achieved at the final moment of time. Previously, the solution of such a problem was studied and described using contour integrals. However, this type of solution is not very convenient for large-dimensional systems, so this article proposes a description of the numerical solution without the use of contour integrals, and also examines the convergence of this numerical solution.

Détail

Keywords: relatively regular matrices, Cauchy problem, Showalter-Sidorov problem, approximations of resolving matrix flows, convergence of the numerical solution.

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