Fourth Order Runge-Kutta and Gill Methods in Numerical Analysis of Predator-Prey Models

Abstract

Purpose of the study: This study aims to solve the numerical solution of the Predator-Prey model using the fourth-order Runge-Kutta and Gill methods, and to determine the profile of the Predator-Prey model solved numerically using the fourth-order Runge-Kutta and Gill methods. Methodology: Schematically, the steps taken in this study are starting from a literature review of the Predator-Prey Model, then solving the Predator-Prey Model using the Fourth-Order Runge-Kutta and Gill Methods, then the program creation step which is continued with program simulation, and finally analysis of the simulation results. Main Findings: From the results of the analysis of the difference in estimates of the fourth-order Runge-Kutta and Gill for predators and prey, there is no significant difference between the two methods in determining a better method in solving the Predator-Prey model. Because the Predator-Prey model cannot be solved analytically, the difference between the two methods cannot be seen from the analytical solution approach. The simulation results using the fourth-order Runge-Kutta and Gill methods show that the greater the value of b, the prey population increases with a value of α > β, and the smaller the values ​​of α and β given, the interaction process between the two populations will slow down and the prey population will increase. Novelty/Originality of this study: can provide information about the profile of the Predator-Prey model which is solved numerically using the fourth-order Runge-Kutta and Gill methods. The combination of these two methods to solve the Predator-Prey model is the novelty of this study