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Extended convergence ball for an efficient eighth order method using only the first derivative

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Abstract

We develop an extended convergence ball for an efficient eighth order method to obtain numerical solutions of Banach space valued nonlinear models. Convergence of this algorithm has previously been shown using assumptions up to the ninth derivative. However, in our convergence theorem, we use only the first derivative. As a consequence, in contrast to previous ideas, the results on calculable error bounds, convergence radius and uniqueness zone for the solution are provided. Furthermore, this scheme is applied to several complex polynomials and related attraction basins are displayed. The results of numerical tests are presented and compared with the earlier technique. We arrive at the conclusion that the suggested analysis produces much larger convergence radii in all tests. Hence, we expand the convergence domain of this iterative formula.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Department of Mathematics, Kalinga Institute of Industrial Technology, Bhubaneswar, Odisha, 751024, India

    Debasis Sharma

  3. Department of Computing and Technology, Cameron University, Lawton, OK, 73505, USA

    Christopher I. Argyros

  4. Department of Mathematics, Fakir Mohan University, Balasore, Odisha, 756020, India

    Sanjaya Kumar Parhi

  5. Department of Mathematics, IIIT Bhubaneswar, Bhubaneswar, Odisha, 751003, India

    Shanta Kumari Sunanda

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  1. Ioannis K. Argyros
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  2. Debasis Sharma
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  4. Sanjaya Kumar Parhi
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  5. Shanta Kumari Sunanda
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Argyros, I.K., Sharma, D., Argyros, C.I. et al. Extended convergence ball for an efficient eighth order method using only the first derivative. SeMA 80, 319–331 (2023). https://doi.org/10.1007/s40324-022-00287-0

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  • DOI: https://doi.org/10.1007/s40324-022-00287-0

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