On the convergence of a novel seventh convergence order schemes for solving equations

Abstract

We study the local convergence of a seventh order scheme for solving nonlinear equations for Banach space valued equations. This is done by using assumptions only on the first derivative that does appear on the schemes, whereas in earlier works up to the eighth derivative (not on the scheme) are used to establish the convergence (not on the scheme). Our technique is so general that it can be used to extend the usage of other schemes along the same lines. © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.