Numerical Methods: Comparative Analysis of Different Methods for Non-Linear Equations

Abstract

Solving nonlinear equations analytically becomes increasingly complex as functions grow in difficulty or when multiple nonlinear components are involved. This study aims to address that challenge by applying and comparing two well-established numerical methods—the Bisection Method and the False Position Method—in approximating the real roots of nonlinear equations. These iterative techniques are evaluated based on their accuracy, convergence rate, and computational efficiency. Specifically, the study investigates the number of iterations required, the magnitude of relative errors, and the number of significant digits in the final approximations. The results show that while both methods are capable of reaching the desired tolerance, the False Position Method converges faster and yields a higher accuracy score. The findings contribute to the practical selection of numerical methods by providing a comparative analysis that guides users in choosing the most appropriate technique based on the nature of the nonlinear function.