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

  • Elpianora Elpianora STKIP Muhammadiyah Sungai Penuh
  • Mark Berou University of the Philippines Diliman
  • Xianfen Kong Xi’an Jiaotong-Liverpool University
  • Kanal Hun Royal University of Phnom Penh
  • Elham Azadegan Islamic Azad University-Karaj Branch
Keywords: Fourth Order Runge-Kutta, Numerical Analysis, Predator-Prey, Runge-Kutta Gill

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

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Published
2024-12-17
How to Cite
Elpianora, E., Berou, M., Kong, X., Hun, K., & Azadegan, E. (2024). Fourth Order Runge-Kutta and Gill Methods in Numerical Analysis of Predator-Prey Models. Interval: Indonesian Journal of Mathematical Education, 2(2), 164-177. https://doi.org/10.37251/ijome.v2i2.1366
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Articles