Local Convergence for Multi-Step High Order Solvers under Weak Conditions

Our aim in this article is to suggest an extended local convergence study for a class of multi-step solvers for nonlinear equations valued in a Banach space. In comparison to previous studies, where they adopt hypotheses up to 7th Fŕechet-derivative, we restrict the hypotheses to only first-order de...

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Bibliographic Details
Main Authors: Ramandeep Behl, Ioannis K. Argyros
Format: Article
Language:English
Published: MDPI AG 2020-02-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/8/2/179
Description
Summary:Our aim in this article is to suggest an extended local convergence study for a class of multi-step solvers for nonlinear equations valued in a Banach space. In comparison to previous studies, where they adopt hypotheses up to 7th Fŕechet-derivative, we restrict the hypotheses to only first-order derivative of considered operators and Lipschitz constants. Hence, we enlarge the suitability region of these solvers along with computable radii of convergence. In the end of this study, we choose a variety of numerical problems which illustrate that our works are applicable but not earlier to solve nonlinear problems.
ISSN:2227-7390