Modeling Population Growth in a Rural Area Using the Fourth-Order Runge-Kutta Method

Abstract

Population modeling remains a critical concern in understanding demographic trends, resource planning, and sustainable development, especially in developing nations such as Nepal. In rural regions where data collection may be sparse, numerical techniques provide an invaluable tool for modeling growth. This study aims to analyze the population growth dynamics of a rural municipality in Nepal by employing the fourth-order Runge-Kutta (RK4) method—a widely accepted numerical technique for solving ordinary differential equations (ODEs). The logistic growth model, which accounts for a population’s carrying capacity, is selected as the base differential equation. Using authentic demographic data from Nepal’s Central Bureau of Statistics (CBS) for the years 1991–2021, this paper demonstrates the implementation of the RK4 algorithm to approximate population values across selected intervals. The results exhibit a close fit to the actual population data, with a minimal relative error, reinforcing the accuracy and practical utility of RK4 in modeling real-world rural population systems. The analysis not only offers insights into the rate and limit of growth but also suggests potential for future forecasting and planning