A seventh-order convergent Newton-type method for solving nonlinear equations

Abstract

In this paper, we present a seventh-order convergent Newton-type method for solving nonlinear equations which is free from second derivative. At each iteration it requires three evaluations of the given function and two evaluation of its first derivative. Therefore its efficiency index is equal to equation which is better than that of Newton's method √2. Several examples demonstrate that the algorithm is more efficient than classical Newton's method and other existing methods.