A Numerical Comparison of the Bisection Method and Newton’s Method

This paper presents a numerical comparison of two classical root-finding algorithms: the bisection method and Newton’s method. Both methods are applied to a selected nonlinear equation in order to analyze their convergence behavior, numerical stability, and practical efficiency under identical conditions. The comparison is based on a simple numerical experiment using a fixed stopping criterion and well-defined initial conditions. The results demonstrate the guaranteed but relatively slow linear convergence of the bisection method, as well as the fast quadratic convergence of Newton’s method when a suitable initial approximation is available. The study highlights the fundamental trade-off between robustness and efficiency in numerical root-finding and provides a clear and accessible illustration of the practical differences between these widely used methods.