An Optimal Family of Eighth-Order Iterative Methods with an Inverse Interpolatory Rational Function Error Corrector for Nonlinear Equations

Abstract

The main motivation of this study is to propose an optimal scheme with an inverse interpolatory rational function error corrector in a general way that can be applied to any existing optimal multi-point fourth-order iterative scheme whose first sub step employs Newton’s method to further produce optimal eighth-order iterative schemes. In addition, we also discussed the theoretical and computational properties of our scheme. Variety of concrete numerical experiments and basins of attraction are extensively treated to confirm the theoretical development.