Population Growth Forecasting Using the Verhulst Logistic Model and Numerical Techniques

This project delves into the realm of population growth modelling and the practical application of numerical methods in predicting population dynamics. Focusing on the Pearl-VerhulstPearl-Verhulst Logistic growth model, we explore the integration of intrinsic growth and environmental constraints. Leveraging MATLAB as a powerful mathematical software tool, we employ the 4th Order Runge-Kutta4th Order Runge-Kutta and Two-step Adams-Bashforth methodsTwo-step Adams-Bashforth methods to solve the differential equations that govern population growth. The project's initiation underscores the critical need for accurate population growth estimation across various disciplines, from ecology to economics. The historical roots of the Pearl-Verhulst model, developed in the early nineteenth century, emphasize its enduring relevance. Our central endeavour involves practically implementing these numerical methods, offering insights into how they can be effectively utilised in population modelling scenarios. A pivotal component of this project is the comparative analysis of the results produced by the two numerical methods. This analysis unveils the consistency and suitability of each method for different applications. The multi-faceted nature of our project's chosen problem underscores its significance. Accurate population growthPopulation growth predictions are essential for informed decision-making, and the comparative analysis sheds light on the method that best aligns with specific research requirements. Furthermore, our exploration of MATLAB's capabilities extends to other domains where numerical problem-solving plays a pivotal role. In the subsequent sections, we provide comprehensive examinations of each problem statement, delivering theoretical foundations, practical demonstrations, and meticulous analyses. This project aims to contribute to the broader understanding of numerical methods, their efficacy in population modelling, and their application in solving complex mathematical challenges across diverse fields.