METODE BRACKETING VERSUS OPEN DALAM MENEMUKAN NOL FUNGSI DENGAN MATLAB

Finding the roots of a function is a fundamental problem in numerical analysis in various scientific and engineering applications. The Bracketing method (Bisection, Regula Falsi) and the Open method (Newton-Raphson, Secant) have been developed to solve this problem. This research aims to compare the performance of the four methods in finding the roots of polynomial and transcendental functions. Implementation was carried out using MATLAB to ensure computational efficiency and validity. Four numerical methods were tested on polynomial and transcendental functions with evaluation criteria including the number of iterations required to achieve a certain tolerance, the accuracy of the roots obtained, and stability against variations in initial values. The results found, the Secant Method has a speed almost equivalent to Newton-Raphson, without requiring function derivatives, making it more flexible. Regula Falsi is faster than Bisection but can experience stagnation under certain conditions. Bisection always converges with high stability, but requires more iterations than other methods. For polynomial functions, Newton-Raphson and Secant are more efficient, while for transcendental functions, Secant is a more practical alternative to Newton-Raphson if the derivative is difficult to calculate. No method is completely superior in all aspects. Newton-Raphson and Secant are recommended for computational efficiency, while Bisection and Regula Falsi are preferred if stability and certainty of convergence are preferred.