Neural Network Algorithm for Solving the Differential Equation of Interindustry Balance

Abstract

One of the methods for studying the description and study of structural economics is the description of a mathematical model using a system of differential equations. In the article we propose an algorithm for bringing a system of differential equations to canonical form. We are developing a neural network algorithm for solving differential equations. We study how errors in statistical data affect the solutions of the differential equation and the accuracy of the forecast. A theorem has been proven that allows one to estimate the error limits of the resulting forecast. The properties of non-negative matrices are studied, an algorithm is proposed for finding the desired solution to the differential equation under the conditions of existing rounding errors in statistical data.