Analyzing the Impact of Birth and Death Rates on Population Growth Using Modified Euler Method: A Case Study of Dhanusha District

Abstract

This research examines the impact of birth and death rates on population growth in Nepal's Dhanusha District using the Modified Euler Method, a refined numerical technique for solving ordinary differential equations. Drawing on official population data from the 2011 census, the study applies a constant net growth rate to project population dynamics through 2021. This mathematical approach is used to compute yearly population figures and analyze demographic trends over the decade. The results validate the Modified Euler Method as an accurate and practical numerical approach for short-term demographic forecasting, demonstrating both the sensitivity and stability of population projections based on empirical birth and death data. The study contributes a replicable framework for population modeling in similar developing contexts, emphasizing the utility of computational mathematics in real-world social planning.