BALL COMPARISON OF THREE METHODS OF CONVERGENCE ORDER SIX UNDER THE SAME SET OF CONDITIONS

IOANNIS K.  ARGYROS; SANTHOSH  GEORGE

BALL COMPARISON OF THREE METHODS OF CONVERGENCE ORDER SIX UNDER THE SAME SET OF CONDITIONS

Authors

IOANNIS K. ARGYROS Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
SANTHOSH GEORGE Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025

Keywords:

High order methods, Banach space, local convergence, $(\omega)$-conditions

Abstract

The aim of this paper is to compare the convergence radii of three methods of convergence order six under the same conditions. Moreover, we expand the applicability of these methods using only the first derivative in contrast to earlier works using hypotheses on derivatives up to order seven although these derivatives do not appear in the methods. Numerical examples complete this study.