Fifth And Eighth Order Iterative Methods For Solving Nonlinear Equations With Their Basins Of Attraction

Abstract

In this paper, we propose and discuss multi point iterative methods for solving nonlinear equations. These methods are based on classical newton method and have fifth and eighth order convergence. The convergence analysis of proposed methods have proved. The effectiveness and performance of the new iterative methods have been tested and compared with few existing equivalent methods on various numerical examples. Finally, the basins of attraction for various polynomials are demonstrated to display the stability of method with respect to the initial point.