An efficient derivative free iterative method for solving systems of nonlinear equations

Abstract

We present a derivative free method of fourth order convergence for solving systems of nonlinear equations. The method consists of two steps of which first step is the well-known Traub's method. First-order divided difference operator for functions of several variables and direct computation by Taylor's expansion are used to prove the local convergence order. Computational ef- ficiency of new method in its general form is discussed and is compared with existing methods of similar nature. It is proved that for large systems the new method is more efficient. Some numerical tests are performed to com- pare proposed method with existing methods and to confirm the theoretical results.