Enhancing the practicality of Newton–Cotes iterative method

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dc.contributor.authorSadananda, R.
dc.contributor.authorGeorge, S.
dc.contributor.authorKunnarath, A.
dc.contributor.authorPadikkal, J.
dc.contributor.authorArgyros, I.K.
dc.date.accessioned2026-02-04T12:26:22Z
dc.date.issued2023
dc.description.abstractThe new Newton-type iterative method developed by Khirallah et al. (Bull Math Sci Appl 2:01–14, 2012), is shown to be of the convergence order three, without the application of Taylor series expansion. Our analysis is based on the assumptions on second order derivative of the involved operator, unlike the earlier studies. Moreover, this technique is extended to methods of higher order of convergence, five and six. This paper also verifies the theoretical approach using numerical examples and comparisons, in addition to the visualization of Julia and Fatou sets of the corresponding methods. © 2023, The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics.
dc.identifier.citationJournal of Applied Mathematics and Computing, 2023, 69, 4, pp. 3359-3389
dc.identifier.issn15985865
dc.identifier.urihttps://doi.org/10.1007/s12190-023-01886-4
dc.identifier.urihttps://idr.nitk.ac.in/handle/123456789/21795
dc.publisherInstitute for Ionics
dc.subjectBanach spaces
dc.subjectNumerical methods
dc.subjectTaylor series
dc.subjectConvergence order
dc.subjectFrechet derivative
dc.subjectHigh-order
dc.subjectHigher-order
dc.subjectNewton Cotes method
dc.subjectNewton-Cotes
dc.subjectOrder of convergence
dc.subjectSecond-order derivative
dc.subjectTaylor's expansion
dc.subjectTaylor's series expansion
dc.subjectIterative methods
dc.titleEnhancing the practicality of Newton–Cotes iterative method

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