Suatu Kelas Kaedah Optimum Bak Steffensen Bebas Terbitan untuk Punca Berganda

The main objective of this paper was to find multiple roots for nonlinear equations. The three-step iteration method is modified to be derivative free which maintains an optimum convergence of eight. The derivative-free iteration scheme was developed based on the Steffensen-like method and finite difference concept. The modified method satisfies the optimal convergence of Kung-Traub's conjectures as shown in the convergence analysis. The iteration scheme can compete with the existing iteration methods in terms of free derivatives. The efficiency index has reached the value E = 1.682 and is better than the classical Newton method, E = 1.414. Numerical experiments have been done to determine the effectiveness of the iteration scheme in finding multiple roots and also simple roots.