On the Local Convergence of an Eighth-order Method for Solving Nonlinear Equations

Abstract

Abstract. We present a local convergence analysis of an eighthorder method for approximating a locally unique solution of a nonlinear equation. Earlier studies such as have shown convergence of these methods under hypotheses up to the seventh derivative of the function although only the first derivative appears in the method. In this study, we expand the applicability of these methods using only hypotheses up to the first derivative of the function. This way the applicability of these methods is extended under weaker hypotheses. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.