Geodesic
Local convergence for multistep high order methods under weak conditions
Ioannis K. Argyros1 ; Ramandeep Behl2 ; Daniel González3 ; S. S. Motsa4
1 Department of Mathematics Sciences Cameron University Lawton, OK 73505, U.S.A. <a href="https://orcid.org/0000-0002-9189-9298">ORCID: 0000-0002-9189-9298</a>
2 School of Mathematics Statistics and Computer Sciences University of KwaZulu-Natal Private Bag X01, Scottsville 3209 Pietermaritzburg, South Africa <a href="https://orcid.org/0000-0003-1505-8945">ORCID: 0000-0003-1505-8945</a>
3 Escuela de Ciencias Físicas y Matemáticas Universidad de Las Américas Quito 170125, Ecuador <a href="https://orcid.org/0000-0001-5282-7251">ORCID: 0000-0001-5282-7251</a>
4 School of Mathematics Statistics and Computer Sciences University of KwaZulu-Natal Private Bag X01, Scottsville 3209 Pietermaritzburg, South Africa
Applicationes Mathematicae, Tome 47 (2020) no. 2, pp. 293-304.

Voir la notice de l'article provenant de 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.
DOI : 10.4064/am2374-1-2019
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

Ioannis K. Argyros 1 ; Ramandeep Behl 2 ; Daniel González 3 ; S. S. Motsa 4

1 Department of Mathematics Sciences Cameron University Lawton, OK 73505, U.S.A. <a href="https://orcid.org/0000-0002-9189-9298">ORCID: 0000-0002-9189-9298</a>
2 School of Mathematics Statistics and Computer Sciences University of KwaZulu-Natal Private Bag X01, Scottsville 3209 Pietermaritzburg, South Africa <a href="https://orcid.org/0000-0003-1505-8945">ORCID: 0000-0003-1505-8945</a>
3 Escuela de Ciencias Físicas y Matemáticas Universidad de Las Américas Quito 170125, Ecuador <a href="https://orcid.org/0000-0001-5282-7251">ORCID: 0000-0001-5282-7251</a>
4 School of Mathematics Statistics and Computer Sciences University of KwaZulu-Natal Private Bag X01, Scottsville 3209 Pietermaritzburg, South Africa 
@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},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2020},
     doi = {10.4064/am2374-1-2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am2374-1-2019/}
}
TY  - JOUR
AU  - Ioannis K. Argyros
AU  - Ramandeep Behl
AU  - Daniel González
AU  - S. S. Motsa
TI  - Local convergence for multistep high order methods under weak conditions
JO  - Applicationes Mathematicae
PY  - 2020
SP  - 293
EP  - 304
VL  - 47
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am2374-1-2019/
DO  - 10.4064/am2374-1-2019
LA  - en
ID  - 10_4064_am2374_1_2019
ER  - 
%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
%I mathdoc
%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. http://geodesic.mathdoc.fr/articles/10.4064/am2374-1-2019/

Cité par Sources :