Expanding the applicability of a fifth-order convergent method in a Banach space under weak conditions
Volume 45 / 2018
Applicationes Mathematicae 45 (2018), 91-101
MSC: 65G99, 65H10, 47J25, 47J05.
DOI: 10.4064/am2303-11-2016
Published online: 28 May 2018
Abstract
We present a local convergence analysis for a fifth-order convergent method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In contrast to the earlier studies using hypotheses up to the fifth Fréchet derivative, we only use hypotheses on the first-order Fréchet derivative and Lipschitz constants. In this way, we not only expand the applicability of the methods but also evaluate the theoretical radius of convergence of these methods. Finally, a variety of concrete numerical examples demonstrate that our results even apply to solve those nonlinear equations where earlier studies cannot apply.
