MATHEMATICAL MODEL AND COMPUTATIONAL ALGORITHM FOR SOLVING THE PROBLEM OF THE COEXISTENCE OF DIFFERENT GROUPS OF PEOPLE IN AN URBAN ENVIRONMENT
Abstract
The article is devoted to the currently relevant problem of the development and dynamics of the population in urban formation from the point of view of spatial-dynamic approximation. The population is divided by different groups according to their economic and individual characteristics. For example, the population can be classified according to genetic and phenotypic traits, 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 in any urban type of formation. 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. Special 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 considering the selected assumptions regarding two specific groups of the population. As an example, the author finds conditions that lead to segregation of groups. For clarity, high-quality pictures of changes in the composition of selected groups in the occupied territory, obtained after numerical modeling, are presented. 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 the program of using spatial economics to describe real processes in urban formations. In the future, it will be interesting to investigate the influence of stochastic processes on the constructed model, and also to pay special attention to the search for parameters of regimes that meet the most pressing problems of interaction between groups of the population.
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