New Eighth and Sixteenth Order Iterative Methods to Solve Nonlinear Equations

Abstract

In this work we proposed two new higher order iterative methods to solve nonlinear equations. These methods based on the method Rafiullah (Numer Anal Appl 4(3):239–243, 2011) which is fifth-order. The Lagrange interpolation is used to improve the convergence order and efficiency index of the method. Convergence order of new methods are proved analytically. Some test problems are given to show the efficiency of the proposed methods.