Numerical solution of Lotka-Volterra Competitive model by using Euler and Fourth order Runge-Kutta methods

This study compares the Euler and Fourth order Runge-Kutta numerical methods for solving the Lotka-Volterra Competitive model. The objective of the study is to analyze the competitive interactions that occurred between lions Panthera leo and leopards P. pardus in the Sabi Sand Game Reserve, South Africa. Numerical approximation tests evaluate the reliability and precision of both methods applied to the logistic equation. The fmdings indicate that the RK method provides a superior approximation, outperforming the Euler method. Graphical representation of the numerical approximations in Wolfram Mathematica 12. l confirms the close alignment between the RK method with exact values. The study also explores the impact of carrying capacity on the dynamics of interspecies competition. Carrying capacity refers to the maximum population size that a species can sustain indefinitely, considering factors like food, habitat, water, and others. The results demonstrate that a larger carrying capacity corresponds to a greater ability for a species to thrive and survive in competitive environments. Moreover, this study showcases the practical application of numerical approximation as a predictive tool for understanding species interactions. By using data simulation to emulate real-world scenarios, researchers can accurately predict the outcomes of interspecific competition without the need for prolonged experiments.