- Tytuł:
- Local convergence of a multi-step high order method with divided differences under hypotheses on the first derivative
- Autorzy:
-
Argyros, Ioannis K.
George, Santhosh - Powiązania:
- https://bibliotekanauki.pl/articles/744644.pdf
- Data publikacji:
- 2017-12-01
- Wydawca:
- Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
- Tematy:
-
Multi-step method
restricted convergence domain
radius of convergence
local convergence - Opis:
- 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.
- Źródło:
-
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2017, 16
2300-133X - Pojawia się w:
- Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł