New Optimal Family of Iterative Methods for Solving Nonlinear Equations

Motivated by the results of J. Kou, et al. 2007 [1] which is a family of iterative methods having third order of convergence in general and optimal fourth order of convergence for a particlue case, in this paper, a new class of optimal fourth-order iterative methods is obtained based on that and by using the weight function approach. The convergence analysis of our new class of iterative methods is presented in this paper. Moreover, several numerical examples are considered and compared with the available methods in the literature to confirm our theoretical results.