Extended comparison between two Newton–Jarratt sixth order schemes for nonlinear models under the same set of conditions
Volume 50 / 2023
Applicationes Mathematicae 50 (2023), 67-79
MSC: Primary 65E99; Secondary 65H10, 49M15.
DOI: 10.4064/am2437-2-2023
Published online: 27 March 2023
Abstract
Two sixth order convergence order schemes are compared and extended to solve Banach space valued models. Earlier studies have used derivatives and Taylor expansions up to order seven to show the convergence order in a finite-dimensional Euclidean space setting. We compute the order by finding computational convergence order or approximate computational convergence order, and condition only on the derivative that is present in the schemes. Moreover, a computable convergence radius, upper error bounds and uniqueness of the solution are provided. Numerical applications illustrate the theoretical results.
