Laplace Transform and Fourth Order Runge-Kutta Method for Solving Population Growth Models

Abstract

There are two population growth models, which are the exponential model and logistic model in this project. These two population models are solved using Laplace transform and the fourth order Runge-Kutta method. Laplace transform is used directly to solve exponential model because it is a linear ordinary differential equation. Since the logistic model is a nonlinear ordinary differential equation, Adomian polynomials are applied to solve the problem by Laplace transform. The MATLAB software is used to calculate the solutions by the RK4 method. Two step sizes are considered, which are  and . The absolute errors are calculated and the results are summarised in graphs to compare the results of solving population growth models using Laplace transform and RK4 method.