COMPUTATIONAL ASPECTS OF SOLVING THE PROBLEM OF INTERACTION OF POPULATION GROUPS IN URBAN EDUCATION

Abstract

The article is devoted to the currently actual problem of the development and dynamics of the population in urban education from the point of view of spatial-dynamic approximation. The population is divided into different groups according to their economic and individual characteristics. For example, the population can be classified according to genetic and phenotypic characteristics, according to the level of income or education. The question of the peaceful and effective interaction of groups with each other is one of the most important tasks within any urban type of education. The author describes the problem of the interaction of two groups at a qualitative level using a system of two non-stationary nonlinear differential equations of diffusion type. Particular attention is paid to the disclosure of the numerical solution scheme of the selected model: the use of an explicit (in time) difference scheme of the “predictor-corrector” type has been analyzed in detail. In addition, the author conducts a series of computational experiments taking into account the selected assumptions regarding two specific groups of the population. Separately, the solution of the stochastic case and the features of its software implementation are considered. Based on the results of the study, the possibility of the applicability of the new approach to the problems of urban studies is substantiated. This work is the first step in the implementation of a program of using spatial economics to describe real processes in urban formations.