Perbandingan Metode Bisection dan Metode Newton-Raphson untuk Menyelesaikan Persamaan Tak Linear pada Model Volume Kotak Tanpa Tutup

Abstract

Determining the corner cut size in the construction of an open-top box can be formulated as a nonlinear equation, requiring numerical methods to obtain its solution. This study aims to determine the corner cut size that produces the specified box volume and to compare the performance of the Bisection Method and the Newton-Raphson Method in solving the mathematical model. A numerical approach was employed by formulating the volume model of an open-top box made from a 30 cm × 30 cm origami sheet. The target volumes analyzed were 3800 cm³, 4100 cm³, 4300 cm³, 4500 cm³, and 4700 cm³. The initial interval for the Bisection Method and the initial guess for the Newton–Raphson Method were determined using GeoGebra, while the iterative computations were performed in Microsoft Excel with an error tolerance of (10^{-3}). The results show that both methods successfully produced the same root values for all target volumes and satisfied the specified error tolerance. However, the Newton-Raphson Method required only two to four iterations to reach convergence, whereas the Bisection Method required 18 to 29 iterations to achieve the same level of accuracy. Therefore, the Newton-Raphson Method is more efficient in terms of the number of iterations and computational time, while the Bisection Method is simpler to implement and remains stable as long as the initial interval satisfies the sign-change condition.