A simple yet efficient derivative free family of seventh order methods for systems of nonlinear equations

Abstract

Based on Traub-Steffensen scheme, we present a family of seventh order derivative free methods for solving systems of nonlinear equations. Computational efficiency of the methods of the family is considered and compared with existing methods of similar nature. Furthermore, numerical experiments are performed to confirm the theoretical results concerning order of convergence and computational efficiency. It is shown that, in general, the proposed methods are more efficient than their existing counterparts.