FORECASTING POPULATION DENSITY AND WATER RESOURCES IN UZBEKISTAN FOR 2025–2030: A NUMERICAL APPROACH USING THE TRIDIAGONAL MATRIX ALGORITHM

This study presents a mathematical model to forecast the dynamics of population density uuu and water resources vvv in Uzbekistan from 2025 to 2030, based on historical data from 2010 to 2024. A system of nonlinear partial differential equations (PDEs) is employed to describe the interaction between population growth and water consumption. The model is solved numerically using an implicit finite difference scheme and the tridiagonal matrix algorithm (TMA) with an iterative approach, using real data-derived initial conditions and a Gaussian distribution for the spatial representation of population and water resources. By 2030, Uzbekistan’s average population density may reach , while water resources decline to under a baseline scenario, or with a 0.5% reduction in depletion. The study recommends implementing water-saving technologies, such as drip irrigation, to ensure sustainable resource management in Uzbekistan.