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Semilocal convergence of Chebyshev Kurchatov type methods for non-differentiable operators

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Abstract
In this study, the new semilocal convergence for the family of Chebyshev Kurchatov type methods is proposed under weaker conditions. The convergence analysis demands conditions on the initial approximation, auxiliary point, and the underlying operator (Argyros et al. (2017) [10]). By utilizing the notion of auxiliary point in convergence conditions, the convergence domains are obtained where the existing results are not applicable. The theoretical results are validated using numerical examples, such as nonlinear PDE and mixed Hammerstein type integral equations originating in biology, vehicular traffic theory, and queuing theory, to determine the applicability of the proposed framework. The numerical testing shows that the new approach performed better (accurately and converge faster) than Steffensen's method, Chebyshev type methods and two step secant method.
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Description
Publisher
Elsevier
Citation
Computers and Mathematics with Applications 170, pp.275-281
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Mathematics & Statistics
MACSI - Mathematics Application Consortium for Science & Industry
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Singh_2024_Semilocal.pdf
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Keywords
chebyshev kurchatov type methods, recurrence relations, semilocal convergence, convergence balls, integral equations, Information and computing sciences
ULRR Identifiers
https://doi.org/10.34961/researchrepository-ul.26789119
 https://researchrepository.ul.ie/handle/10344/13721
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Funding Information
Sustainable Development Goals
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Article
Rights
https://creativecommons.org/licenses/by-nc-sa/4.0/
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