Applied Research with Two Modified Three-Step Algorithms Based on Double Newton Method for Solving Nonlinear Equations

With the rapid development and wide application of information engineering and applied technology, nonlinear problems become an important direction of research in the field of numerical calculation and analysis. In this paper, we mainly study the iterative methods of nonlinear equations. We present and analyze two modified three-step Newton-type methods based on double Newton method for solving nonlinear equations. One is sixth-order convergent, while the other is seventh-order convergent. Both methods are free from second derivatives. The efficiency indices of the presented methods are 1.4310 and 1.4758, respectively, both of which are better than that of the classical Newton’s method 1.414. Some numerical experiments illustrate the efficiency and performance of the proposed methods.