An iterative method with fifteenth-order convergence to solve systems of nonlinear equations

Abstract

In this article, a modification of Newton’s method with fifteenth-order convergence is presented. The modification of Newton’s method is based on the method of fifth-order convergence of Hu et al. First, we present theoretical preliminaries of the method. Second, we solve some nonlinear equations and then systems of nonlinear equations obtained by means of the finite element method. In contrast to the eleventh-order M. Raza method, the fifteenth-order method needs less function of evaluation per iteration, but the order of convergence increases by four units. Numerical examples are given to show the efficiency of the proposed method.