A new optimal eighth-order iterative technique for solving simple roots of nonlinear equations

In this study, we present an iterative technique of eighth order for solving a non-linear equation. Our proposed method is optimal according to Kung-Traub conjecture, requiring only four function evaluations per iteration for the eighth order technique. We analysed the theoretical aspects of our scheme, thoroughly exploring its convergence properties through the main theorem, which serves to demonstrate the convergence order. To check the practical utility of our optimal iteration functions, we conduct a comparative analysis against existing competitors using standard academic problems. This enables us to highlight the superior performance and e ectiveness of our approach in solving non-linear equations.