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Open AccessArticle

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

1
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 179; https://doi.org/10.3390/math8020179
Received: 19 November 2019 / Revised: 21 January 2020 / Accepted: 24 January 2020 / Published: 2 February 2020
(This article belongs to the Special Issue Computational Methods in Analysis and Applications 2020)
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.
Keywords: local convergence; multi-step iterative solver; Lipschitz constant; order of convergence; Banach space local convergence; multi-step iterative solver; Lipschitz constant; order of convergence; Banach space
MDPI and ACS Style

Behl, R.; Argyros, I.K. Local Convergence for Multi-Step High Order Solvers under Weak Conditions. Mathematics 2020, 8, 179.

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