Extending the applicability of a seventh-order method for equations under generalized conditions
Volume 50 / 2023
Applicationes Mathematicae 50 (2023), 167-175
MSC: Primary 65J20; Secondary 49M15, 74G20, 41A25.
DOI: 10.4064/am2439-2-2023
Published online: 27 March 2023
Abstract
We extend the applicability of a seventh-order method for solving Banach space-valued equations. This is achieved by using generalized conditions on the first derivative which only appears in the method. Earlier works use conditions up to the eighth derivative to establish convergence. Our technique is very general and can be used to extend the applicability of other methods along the same lines.
