Local convergence of an at least sixth-order method in Banach spaces

Abstract

We present a local convergence analysis of an at least sixth-order family of methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. The semilocal convergence analysis of this method was studied by Amat et al. in (Appl Math Comput 206:164 174, 2008; Appl Numer Math 62:833 841, 2012). This work provides computable convergence ball and computable error bounds. Numerical examples are also provided in this study. 2019, Springer Nature Switzerland AG.