Means-based class of modified Weerakoon-Fernando method for determining the zero of nonlinear equation

Abstract

This paper introduces a generalized class of modified Weerakoon and Fernando iterative method (WFM) for determining the zero of equations that are nonlinear. The idea applied in the modification, involves the composition of a perturbed Newton method with a corrector iterative function that is based on parametric bi-variate rational function of degree one and a power means generating function. The convergence analysis on the developed class of methods, shows that it is of convergence order four with efficiency index of 1.5874. Some existing modified WFM were established to be concrete members of the developed class of methods. Numerical results obtained when the new methods were implemented are provided to compare their effectiveness and efficiency.