https://doi.org/10.65770/PWEL5664
ABSTRACT
This study evaluates and compares the performance of the fourth-order Runge-Kutta (RK4) method against the adaptive Runge-Kutta-Fehlberg 45 (RKF45) method in solving a logistic growth model to predict population dynamics in West Java Province. Growth rate parameters and carrying capacities were estimated through curve-fitting optimization based on historical demographic data from Statistics Indonesia. The performance of both numerical schemes was rigorously assessed using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) metrics. The empirical results demonstrate that the adaptive RKF45 method significantly outperforms the fixed-step RK4 approach in terms of precision, yielding substantially lower error rates. While the overall predictive accuracy remains robust, the logistic model exhibited minor deviations in response to abrupt population fluctuations caused by the COVID-19 pandemic. Ultimately, the inherent flexibility of RKF45 in dynamically adjusting step sizes renders it a highly recommended instrument for accurate demographic forecasting. Implementing such computational methods provides a strategic framework for regional governments in formulating infrastructure planning and promoting sustainable development for the future.
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