Modeling the Spruce Budworm Population: A Numerical Approach Using Heun and Runge-Kutta Methods

Purpose of the study: The purpose of this study is to determine the numerical solution of the spruce caterpillar model using the Heun method and the Third Order Runge-Kutta method, as well as to analyze the errors associated with both methods. Methodology: The type of research used in this study is library research. In this study, the data will be analyzed numerically from the data entry stage, data processing and results. The results obtained are from the Heun programming method and the Runge iteration method that have been determined previously. Kutta-Order Three will produce data with the smallest error in the number of. Main Findings:The results of the study showed the solution of the Pinus Lice model for the initial values ​​of B(t₀) = 2, S(t₀) = 10 cm, E(t₀) = 2 cm, at t = 5 years, with h = 0.05. Using the Heun method, it was obtained that B ≈ 3, S = 14.9058 cm, and E = 1.0047 cm, while the Third Order Runge-Kutta method produced B ≈ 3, S = 14.9057 cm, and E = 1.0046 cm. The error calculation showed that the B error was smaller with the Heun method, while the S and E errors were smaller with the Third Order Runge-Kutta method. Novelty/Originality of this study: The novelty of this study lies in the comparative analysis of the errors of the Heun Method and the Third Order Runge-Kutta Method in modeling the dynamics of spruce budworm populations with specific biological parameters.