An Efficient Twelfth-Order Iterative Method to Solve Nonlinear Equations with Applications

This study proposes an effective, derivative-free, four-step iterative method for zero-finding nonlinear equations. There are five functional evaluations needed for this strategy. The suggested approach possesses twelfth-order convergence, according to the convergence study. We use six real-world application issues from physics, chemical engineering, and medical research to demonstrate the applicability of the suggested approach. The numerical outcomes show that the new method outperforms the earlier schemes in the literature regarding performance, adaptability, and efficiency.