Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative

Ioannis K. Argyros; Santhosh George

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2017)

  • Volume: 16, Issue: 1, page 41-50
  • ISSN: 2300-133X

Abstract

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This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is used to prove the convergence of the method. That restricts the applicability of the method. In this paper we extended the applicability of the sixth-order multi-step method by using only hypotheses on the first derivative of the operator involved. Our convergence conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot be applied to solve equations but our results can be applied are also given in this study.

How to cite

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Ioannis K. Argyros, and Santhosh George. "Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 16.1 (2017): 41-50. <http://eudml.org/doc/288493>.

@article{IoannisK2017,
abstract = {This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is used to prove the convergence of the method. That restricts the applicability of the method. In this paper we extended the applicability of the sixth-order multi-step method by using only hypotheses on the first derivative of the operator involved. Our convergence conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot be applied to solve equations but our results can be applied are also given in this study.},
author = {Ioannis K. Argyros, Santhosh George},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Multi-step method; restricted convergence domain; radius of convergence; local convergence},
language = {eng},
number = {1},
pages = {41-50},
title = {Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative},
url = {http://eudml.org/doc/288493},
volume = {16},
year = {2017},
}

TY - JOUR
AU - Ioannis K. Argyros
AU - Santhosh George
TI - Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2017
VL - 16
IS - 1
SP - 41
EP - 50
AB - This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is used to prove the convergence of the method. That restricts the applicability of the method. In this paper we extended the applicability of the sixth-order multi-step method by using only hypotheses on the first derivative of the operator involved. Our convergence conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot be applied to solve equations but our results can be applied are also given in this study.
LA - eng
KW - Multi-step method; restricted convergence domain; radius of convergence; local convergence
UR - http://eudml.org/doc/288493
ER -

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