Comparative Analysis of the Regula Falsi and Secant Methods for Numerically Solving the Roots of Nonlinear Equations

Dwi Suryo Putro, Syaharuddin Syaharuddin

Abstract


Abstract: This study aims to analyze and compare the effectiveness of two numerical methods, namely Regula Falsi method and Secant method, in solving the roots of non-linear equations. The non-linear equations used in this study include various types of functions, such as polynomial, trigonometric, exponential, and logarithmic functions. Both methods were tested through numerical simulations using MATLAB software to measure performance based on convergence speed, accuracy of results, and stability of the iteration process. The Regula Falsi method works based on linear interpolation between two points that have different function signs, while the Secant method uses two initial guesses without different sign requirements. The analysis shows that the Regula Falsi method is more stable but has slower convergence, while the Secant method converges faster but is less stable under certain conditions. By considering the advantages and disadvantages of each method, the selection of the optimal method is highly dependent on the characteristics of the function and the given initial conditions. This research contributes to understanding the fundamental differences between the two methods and provides practical guidance for researchers, academics, and practitioners in choosing the right numerical approach to solve various mathematical problems involving non-linear equations.

 


Keywords


Regula Falsi Method, Secant Method, Root Solving, Non-Linear Equations.

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