Jarratt-type methods and their convergence analysis without using Taylor expansion

Indra Bate, Kedarnath Senapati, Santhosh George, Muniyasamy M and Chandhini G

Applied Mathematics and Computation, 2025, vol. 487, issue C

Abstract: In this paper, we study the local convergence analysis of the Jarratt-type iterative methods for solving non-linear equations in the Banach space setting without using the Taylor expansion. Convergence analysis using Taylor series required the operator to be differentiable at least p+1 times, where p is the order of convergence. In our convergence analysis, we do not use the Taylor expansion, so we require only assumptions on the derivatives of the involved operator of order up to three only. Thus, we extended the applicability of the methods under study. Further, we obtained a six-order Jarratt-type method by utilising the method studied by Hueso et al. in 2015. Numerical examples and dynamics of the methods are presented to illustrate the theoretical results.

Keywords: Fréchet derivative; Order of convergence; Jarratt method; Taylor expansion; Non-linear equations; Iterative method (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:487:y:2025:i:c:s0096300324005733

DOI: 10.1016/j.amc.2024.129112

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