A Comparative Analysis of Newton-Raphson and Secant Methods Based on Convergence and Computational Efficiency for Solving Nonlinear Equations

Abstract

This study conducts a comparative evaluation of the Newton-Raphson and Secant methods in solving the non-linear equation f(x) =. Numerical methods are essential for solving equations where analytical methods fail or become inefficient. Among these, the Newton-Raphson and Secant methods are two widely used techniques for solving non-linear equations. This research adopts a quantitative computational approach. Both algorithms were implemented in MATLAB under consistent convergence criteria and stopping conditions, utilizing varying initial approximations. Key performance indicators such as the number of iterations, absolute error, function values at each step, and computational time were recorded. The Newton-Raphson method converged in 10 iterations, requiring approximately 0.00243 seconds, whereas the Secant method achieved convergence in only 5 iterations with a reduced computational time of 0.000329 seconds. Although both methods ultimately identified the same root, the results suggest that the Secant method offers greater computational efficiency, provided that suitable initial guesses are selected.