A highly efficient class of optimal fourth-order methods for solving nonlinear systems

Abstract

In this manuscript, we present a new class of highly efficient two-parameter optimal iterative methods for solving nonlinear systems that generalizes Ostrowski's method, King's Family, Chun's method and KLAM Family in multidimensional context. This class is an extension to systems of the Ermakov's Hyperfamily. The fourth order of convergence of the members of the class is demonstrated, thus obtaining optimal schemes for solving nonlinear systems. The high efficiency of the elements of the class is studied, compared with other known methods of the same order or even higher and some numerical proofs are presented and we analyze it robustness.