Families of Means-Based Modified Newtons Method for Solving Nonlinear Models

Abstract

In literature, the arithmetic mean of the two functions in the denominator of the second step of order three Weerakoon and Fernando (2000) iterative method have been replaced with other different means. However, these actions have not improve its order of convergence. To improve the order of convergence of these modified methods, a generic family of iterative methods that involve two weight functions and a generic consequential function for replacement of means is proposed. The analysis of convergence carried out on the families of methods, shows that they are of fourth order convergence and requires evaluation of three functions per iteration cycle. Further, the flexibility of the weight functions enables the re-discovery of some existing and construction of new families of iterative methods. Some concrete members of the family of methods are applied to solve some nonlinear equations and real life problems that are modeled into nonlinear equations.