Technical report: numerical solution of predator-prey model between fox and rabbit by using Euler Method and Fourth Order Runge-Kutta method / Aina Safina Nordin, Fityah Hazimah Noorzali and Nurul Nurfatiah Halim

According to Hussein (2010), the system of predator-prey are useful and often used in environment science field because they allow researchers to both observe the dynamics of animal population and make prediction as how they will develop over model and explore the trends visible. The purpose in this study is to focus on how to solve the general animal population on Predator-Prey Equation by using two methods which are Euler Method and Fourth-Order Runge-Kutta Method. Rabbits and Foxes are the animals that shows the relationship in the predator-prey. The general objective of this study is to derive Predator-Prey Equation using Eu­ler Method and Fourth Order Runge-Kutta Method for general population of animal and then use the general solution to approximate the number of population of rabbits and foxes based on Predator-Prey Equation. In this study, five estimation of animal population with different starting population is created to observe the trend population by comparing the result obtained by using Euler Method and Fourth Order Runge-Kutta Method and we also studied the effect of changing step size, h for Euler Method and Fourth Order Runge-Kutta Method. In addi­tion, from our study we found that fourth order Runge-Kutta is suitable for solving Simple Predator-Prey. This is because Runge-Kutta also show same pattern with previous finding but with different approximate value. Furthermore, in our findings for the third objective, we obtain the result by changing the step size which is does not produce the same trend visible for animal population.