We introduce a new idea of recurrent functions to provide a new semilocal convergence analysis for two-step Newton-type methods of high efficiency index. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in many interesting cases. Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar type, and a differential equation containing a Green's kernel are also provided.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-4-6,
author = {Ioannis K. Argyros and Sa\"\i d Hilout},
title = {On the convergence of two-step Newton-type methods of high efficiency index},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {465-499},
zbl = {1181.65079},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-4-6}
}
Ioannis K. Argyros; Saïd Hilout. On the convergence of two-step Newton-type methods of high efficiency index. Applicationes Mathematicae, Tome 36 (2009) pp. 465-499. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-4-6/