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

In literature, the arithmetic mean of the two functions in thedenominator 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 improvethe order of convergence of these modified methods, a generic familyof iterative methods that involve two weight functions and a genericconsequential function for replacement of means is proposed. The analysisof convergence carried out on the families of methods, shows that theyare of fourth order convergence and requires evaluation of three functionsper iteration cycle. Further, the flexibility of the weight functions enablesthe re-discovery of some existing and construction of new families of iterativemethods. Some concrete members of the family of methods areapplied to solve some nonlinear equations and real life problems that aremodeled into nonlinear equations.AMS (MOS) Subject Classification Codes:65H05; 65D05KeyWords: Nonlinear Model; Mean-Based;Weight Functions; Iterative Method