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

Ramandeep Behl and Ioannis K. Argyros
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Ramandeep Behl: Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Ioannis K. Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Mathematics, 2020, vol. 8, issue 2, 1-14

Abstract: 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 F?echet-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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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