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Research Article | Open Access

Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems

Xiaofeng Wang, Yufan Yang, Yuping Qin( )
School of Mathematical Sciences, Bohai University, Jinzhou 121000, China
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Abstract

In this paper, the semilocal convergence of the eighth order iterative method is proved in Banach space by using the recursive relation, and the proof process does not need high order derivative. By selecting the appropriate initial point and applying the Lipschitz condition to the first order Fréchet derivative in the whole region, the existence and uniqueness domain are obtained. In addition, the theoretical results of semilocal convergence are applied to two nonlinear systems, and satisfactory results are obtained.

Keywords

nonlinear systemiterative methodrecurrence relationsemilocal convergenceexistence domainunique domain
CLC number: 49M15, 65J15, 65G99

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 22371-22384
DOI: 10.3934/math.20231141

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Cite this article:
Wang X, Yang Y, Qin Y. Semilocal convergence analysis of an eighth order iterative method for solving nonlinear systems. AIMS Mathematics, 2023, 8(9): 22371-22384. https://doi.org/10.3934/math.20231141

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Received: 03 June 2023
Revised: 08 July 2023
Accepted: 11 July 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)