COMPARISON OF NEWTON RAPHSON AND SECANT METHODS TO DETERMINE THE OPTIMAL POINT OF TIKTOK APPLICATION
Abstract
The growth of digital application users generally follows a non-linear pattern that can be modeled using the logistics growth function, which has the characteristic of an inflection point, which is a condition when the growth rate reaches the maximum value. Optimal point determination involves solving non-linear equations that cannot always be solved directly, so a numerical approach is required. This study aims to determine the optimal growth point of TikTok application users and compare the performance of the Newton–Raphson and Secant methods in solving non-linear equations in the logistics model. User growth data was obtained from the Google Play Store and simulated using logistics growth parameters that represent the characteristics of applications with a high level of virality, with analytics solutions as an evaluation reference. The calculation results show that the optimal point of growth of TikTok users is around the 6th week. The Secant method yielded an optimal point estimate of 5.972 with an RMSE value of 0.0150 and a relative error of 0.25%, while the Newton–Raphson method yielded an estimate of 5.773 with an RMSE value of 0.2140 and a relative error of 3.57%. The difference in error rate and convergence stability shows that the Secant method provides a more effective approach in determining the optimal growth point of digital application users based on the logistics model.
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