A MATLAB Program for Solving Volterra’s Population Growth Model Utilizing the Hybrid Upadhyaya Transform and Power Series

Abstract

Volterra's population growth model is a valuable equation for understanding how animal or human populations evolve over time. It accounts for natural growth, competition, and the influence of past populations. Solving this equation manually is challenging; therefore, we developed a comprehensive MATLAB program to streamline the solution process. The program employs two methods: an exact solution for the simplified (linearised) model using the Upadhyaya transform and a power series approximation for the complete nonlinear model. Additionally, it features a highly accurate numerical solution using ode45 for comparison. The code generates a clear table of results and two informative graphs.