Local convergence for multistep high order methods under weak conditions
Volume 47 / 2020
Applicationes Mathematicae 47 (2020), 293-304
MSC: 65G99, 65H10, 47J25, 47J05, 65D10, 65D99.
DOI: 10.4064/am2374-1-2019
Published online: 12 October 2020
Abstract
We present a local convergence analysis for an eighth-order convergent method in order to find a solution of a nonlinear equation in a Banach space setting. In contrast to the earlier studies using hypotheses up to the seventh Fréchet derivative, we use only hypotheses on the first-order Fréchet derivative and Lipschitz constants. This way, we not only expand the applicability of these methods but also propose a computable radius of convergence for these methods. Finally, concrete numerical examples demonstrate that our results apply to nonlinear equations not covered before.
