LOCAL CONVERGENCE OF SOME FIFTH AND SIXTH ORDER ITERATIVE METHODS

Abstract

We present a local convergence analysis for some families of fifth and sixth order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies [19] have used hypotheses on the fifth Fréchet derivative of the operator involved. We use hypotheses only on the first Fréchet derivative in our local convergence analysis. This way, the applicability of these methods is extended. Moreover the radius of convergence and computable error bounds on the distances involved are also given using Lipschitz constants. Numerical examples illustrating the theoretical results are also presented in this study.