Local convergence for multistep high order methods under weak conditions
Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 293-304
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We present a local convergence analysis for an eighth-order convergent method in order to find a solution of a nonlinear equation in a Banach space setting. In contrast to the earlier studies using hypotheses up to the seventh Fréchet derivative, we use only hypotheses on the first-order Fréchet derivative and Lipschitz constants. This way, we not only expand the applicability of these methods but also propose a computable radius of convergence for these methods. Finally, concrete numerical examples demonstrate that our results apply to nonlinear equations not covered before.
Keywords:
present local convergence analysis eighth order convergent method order solution nonlinear equation banach space setting contrast earlier studies using hypotheses seventh chet derivative only hypotheses first order chet derivative lipschitz constants only expand applicability these methods propose computable radius convergence these methods finally concrete numerical examples demonstrate results apply nonlinear equations covered before
Affiliations des auteurs :
Ioannis K. Argyros 1 ; Ramandeep Behl 2 ; Daniel González 3 ; S. S. Motsa 4
@article{10_4064_am2374_1_2019,
author = {Ioannis K. Argyros and Ramandeep Behl and Daniel Gonz\'alez and S. S. Motsa},
title = {Local convergence for multistep high order methods under weak conditions},
journal = {Applicationes Mathematicae},
pages = {293--304},
year = {2020},
volume = {47},
number = {2},
doi = {10.4064/am2374-1-2019},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am2374-1-2019/}
}
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%0 Journal Article %A Ioannis K. Argyros %A Ramandeep Behl %A Daniel González %A S. S. Motsa %T Local convergence for multistep high order methods under weak conditions %J Applicationes Mathematicae %D 2020 %P 293-304 %V 47 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4064/am2374-1-2019/ %R 10.4064/am2374-1-2019 %G en %F 10_4064_am2374_1_2019
Ioannis K. Argyros; Ramandeep Behl; Daniel González; S. S. Motsa. Local convergence for multistep high order methods under weak conditions. Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 293-304. doi: 10.4064/am2374-1-2019
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