Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative
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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | deu |
| Published: |
Sciendo
2017-12-01
|
| Series: | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| Subjects: | |
| Online Access: | http://studmath.up.krakow.pl/index.php/studmath/article/view/253 |
| _version_ | 1818365226744020992 |
|---|---|
| author | Ioannis K. Argyros Santhosh George |
| author_facet | Ioannis K. Argyros Santhosh George |
| author_sort | Ioannis K. Argyros |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T22:16:54Z |
| format | Article |
| id | doaj.art-17aabee0abbf4309839f57b42524410d |
| institution | Directory Open Access Journal |
| issn | 2081-545X 2300-133X |
| language | deu |
| last_indexed | 2024-12-13T22:16:54Z |
| publishDate | 2017-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica |
| spelling | doaj.art-17aabee0abbf4309839f57b42524410d2022-12-21T23:29:29ZdeuSciendoAnnales Universitatis Paedagogicae Cracoviensis: Studia Mathematica2081-545X2300-133X2017-12-0116415010.1515/aupcsm-2017-0003Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivativeIoannis K. Argyros0Santhosh George 1Department of Mathematical Sciences Cameron University Lawton OK 73505 United StatesDepartment of Mathematical and Computational Sciences NIT Karnataka India-575 025, India 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.http://studmath.up.krakow.pl/index.php/studmath/article/view/253Multi-step methodrestricted convergence domainradius of convergencelocal convergence |
| spellingShingle | Ioannis K. Argyros 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 Multi-step method restricted convergence domain radius of convergence local convergence |
| title | Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative |
| title_full | Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative |
| title_fullStr | Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative |
| title_full_unstemmed | Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative |
| title_short | Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative |
| title_sort | local convergence of a multi step high order method with divided differences under hypotheses on the first derivative |
| topic | Multi-step method restricted convergence domain radius of convergence local convergence |
| url | http://studmath.up.krakow.pl/index.php/studmath/article/view/253 |
| work_keys_str_mv | AT ioanniskargyros localconvergenceofamultistephighordermethodwithdivideddifferencesunderhypothesesonthefirstderivative AT santhoshgeorge localconvergenceofamultistephighordermethodwithdivideddifferencesunderhypothesesonthefirstderivative |