A new optimal method of fourth-order convergence for solving nonlinear equations

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. ۱۷ (۲۰۰۰) ۸۷-۹۳]. The method is optimal, as it needs three evaluations per iterate, namely one evaluation of function and two evaluations of rst derivative. So, Kung and Traub's conjecture is fullled. We also perform some numerical tests that conrm the theoretical results and allow us to compare the proposed method with some existing methods of the same type.