Finding the root of nonlinear equations using open method / Nur Adlin Arifah Misni

In the fields of science, engineering, and natural science, practitioners often encounter the question of determining the exact root of a function. It is relatively easier to find the exact root for simple functions compared to complicated ones. Consequently, numerical methods in the form of open methods are frequently employed to approximate the roots of functions. This research aims to approximate the roots of six functions using four different initial values. The tested functions comprise combinations of trigonometric, exponential, and cubic polynomial functions, and the open methods utilized include Newton's method, Steffensen's method, Chebyshev's method, and Halley's method. The results are based on the number of iterations, CPU times, and error analysis with three different tolerance levels. The numerical findings demonstrate that Halley's method is the most effective open method for finding the roots of functions.