Numerical Simulation of Nonlinear Equations by Modified Regula Falsi Method

Abstract

The application of modified Regula Falsi approaches for nonlinear equation solving via numerical simulation is investigated in this research article. Three modified versions the Illinois algorithm, Anderson-Björck method, and Pegasus approach, and our proposed Regula Falsi method along with traditional Regula Falsi's performance are compared in this work. These techniques were tested using a set of several different non-linear equations with an eye toward convergence rates, accuracy, and computational economy. With the proposed method showing the best overall performance in terms of convergence speed and accuracy, results show that the modified approaches much outperform the original Regula Falsi. This work advances numerical analysis by offering understanding of the efficiency of several Regula Falsi modifications for the solution of difficult non-linear equations.