CERTAIN ASPECTS OF MATHEMATICAL MODELLING

Research using models is often the only feasible method for experimental study and solving critical practical problems. Mathematical modeling enables the formalization of complex processes in nature, technology, and society, replacing direct experiments with their analytical and numerical counterparts. This article examines the main stages and challenges in constructing mathematical models, issues of similarity and dimensionless parameters, as well as methods for solving and interpreting numerical calculations. Special attention is given to analyzing difficulties arising from equation nonlinearity, selection of numerical methods, and ensuring solution stability and convergence.