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Local convergence analysis of two iterative methods

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Abstract

In this paper we consider two three-step iterative methods with common first two steps. The convergence order five and six, respectively of these methods are proved using assumptions on the first derivative of the operator involved. We also provide dynamics of these methods

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Acknowledgement

The authors wish to thank the referees for their careful reading of the paper and helpful suggestions that led to improvements in the exposition.

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Authors and Affiliations

  1. Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangaluru, 575 025, India

    Santhosh George & Kedarnath Senapati

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

    Ioannis K. Argyros

  3. Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed to be University, Kumbakonam, 612 001, India

    K. Kanagaraj

Authors
  1. Santhosh George
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  2. Ioannis K. Argyros
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  3. Kedarnath Senapati
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  4. K. Kanagaraj
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Correspondence to K. Kanagaraj.

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Communicated by Samy Ponnusamy.

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George, S., Argyros, I.K., Senapati, K. et al. Local convergence analysis of two iterative methods. J Anal 30, 1497–1508 (2022). https://doi.org/10.1007/s41478-022-00415-z

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  • DOI: https://doi.org/10.1007/s41478-022-00415-z

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