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Enhancing the practicality of Newton–Cotes iterative method

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Abstract

The 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.

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Acknowledgements

The authors Santhosh George, Ajil Kunnarath and Jidesh Padikkal wish to thank the SERB, Govt. of India for the Project No. CRG/2021/004776.

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Authors and Affiliations

  1. Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, 575025, India

    Ramya Sadananda, Santhosh George, Ajil Kunnarath & Jidesh Padikkal

  2. Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

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  1. Ramya Sadananda
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Correspondence to Ramya Sadananda.

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Sadananda, R., George, S., Kunnarath, A. et al. Enhancing the practicality of Newton–Cotes iterative method. J. Appl. Math. Comput. 69, 3359–3389 (2023). https://doi.org/10.1007/s12190-023-01886-4

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  • DOI: https://doi.org/10.1007/s12190-023-01886-4

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