New predictor-corrector type iterative methods for solving nonlinear equations

Abstract

This paper proposes two new predictor-corrector type iterative methods for finding roots of nonlinear equations. These methods are generated by based on the combination of the two well known Bisection method and Newton-Raphson method. Various numerical examples serve to verify the main purpose of these methods and compare the numerical results. Numerical results are also presented to test the convergence rate of these new proposed methods in terms of number of iterations achieved to reach the exact root of any nonlinear equation. These numerical results obtained also indicate that new proposed methods perform better than both well known methods Bisection and Newton-Raphson and also the other methods in literature.