Ball analysis for an efficient sixth convergence order scheme under weaker conditions

Abstract

In this study we consider an ecient sixth order-scheme for solving Banach space valued equations. The convergence criteria in earlier studies involve higher order derivatives limiting applicability of these methods. In this study we use the rst derivative only in our analysis to expand the usage of these schemes. The technique we use can be used on other schemes to obtain the same advantages. Numerical experiments compare favorably our results to earlier ones.