Local convergence comparison between two novel sixth order methods for solving equations-Reference-Cited by-同舟云学术

Local convergence comparison between two novel sixth order methods for solving equations

Published:2019-12-01 Issue:1 Volume:18 Page:5-19
ISSN:2300-133X
Container-title:Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
language:en
Short-container-title:

Author:

Argyros Ioannis K.¹,George Santhosh²

Affiliation:

1. Department of Mathematical Sciences , Cameron University , Lawton , OK 73505 , USA

2. Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka , India -575 025

Abstract

Abstract The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples where the convergence criteria are tested are provided. It turns out that in these examples the criteria in the earlier works are not satisfied, so these results cannot be used to solve equations but our results can be used.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/aupcsm-2019-0001

Reference21 articles.

1. [1] Argyros, Ioannis K., Santhosh George and Alberto Á. Magre?án. “Local convergence for multi-point-parametric Chebyshev-Halley-type methods of high convergence order.” J. Comput. Appl. Math. 282 (2015): 215-224. Cited on 6 and 16.

2. [2] Argyros, Ioannis K., Santhosh George and Narayan Thapa. Mathematical modeling for the solution of equations and systems of equations with applications. Vol. 1. New York: Nova Publishes, 2018. Cited on 6, 9, 12 and 16.

3. [3] Argyros, Ioannis K., Santhosh George and Narayan Thapa. Mathematical modeling for the solution of equations and systems of equations with applications. Vol. 2. New York: Nova Publishes, 2018. Cited on 6, 9 and 12.

4. [4] Argyros, Ioannis K., Munish Kansal and V. Kanwar, V. “Local convergence for multipoint methods using only the first derivative.” SeMA J. 73, no. 4 (2016): 369-378. Cited on 6, 8 and 12.

5. [5] Candela, V. and A. Marquina. “Recurrence relations for rational cubic methods. I. The Halley method.” Computing 44, no. 2 (1990): 169-184. Cited on 6, 8 and 12.