Approximation of the Difference Representation of the Solution by Differential Equations in the Problems of Modeling Atmospheric Air Pollution with Nitrogen Dioxide in Motor Vehicle Exhaust Gases

Two approaches to constructing a mathematical model of the distribution of nitrogen dioxide concentration in a given area of the city are considered. In the first approach, based on solving the problem of identification with the analysis of interval data, an interval difference equation is obtained. With the second approach, this equation is approximated by a differential equation. The need for such an approach is caused by the fact that, in most cases, the coefficients of the difference equation have no physical content. In contrast, Differential equations are more suitable for describing the physics of a process. Among them, partial differential equations are distinguished, where the coefficients in the equation are the coefficients of diffusion of a harmful substance in atmospheric air at different spatial coordinates.