Faculty Publications

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Author: search.filters.author.Argyros, I.K.Subject: search.filters.subject.Iterative method

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    Convergence Analysis of a Fifth-Order Iterative Method Using Recurrence Relations and Conditions on the First Derivative
    (Birkhauser, 2021) George, S.; Argyros, I.K.; Padikkal, P.; Mahapatra, M.; Saeed, M.
    Using conditions on the second Fréchet derivative, fifth order of convergence was established in Singh et al. (Mediterr J Math 13:4219–4235, 2016) for an iterative method. In this paper, we establish fifth order of convergence of the method using assumptions only on the first Fréchet derivative of the involved operator. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.
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    Advances in Nonlinear Variational Inequalities Volume 25 (2022), Number 1, 49-58 Comparing and Extending Two Fourth Order Methods Under the Same Hypotheses for Equations
    (International Publications, 2022) Argyros, I.K.; George, S.; Argyros, C.I.
    We compare and extend two fourth order methods for nonlinear equations. Our convergence analysis used assumptions only on the first derivative. Earlier studies have used hypotheses up to the fifth derivative, limiting the applicability of the method. Numerical examples complete the article. © 2022, International Publications. All rights reserved.
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    Local convergence analysis of two iterative methods
    (Springer Science and Business Media B.V., 2022) George, S.; Argyros, I.K.; Senapati, K.; Kanagaraj, K.
    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 © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.
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    On the semilocal convergence analysis of a seventh order four step method for solving nonlinear equations
    (Ptolemy Scientific Research Press, 2024) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.I.
    We provide a semi-local convergence analysis of a seventh order four step method for solving nonlinear problems. Using majorizing sequences and under conditions on the first derivative, we provide sufficient convergence criteria, error bounds on the distances involved and uniqueness. Earlier convergence results have used the eighth derivative not on this method to show convergence. Hence, limiting its applicability. © 2024 by the authors; licensee PSRP, Lahore, Pakistan.
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    Extended convergence for two-step methods with non-differentiable parts in Banach spaces
    (Springer Science and Business Media B.V., 2024) Argyros, I.K.; George, S.; Senapati, K.
    In this study, we have extended the applicability of two-step methods with non-differentiable parts for solving nonlinear equations defined in Banach spaces. The convergence analysis uses conditions weaker than the ones in earlier studies. Other advantages include computable a priori error distances based on generalized conditions, an extended region of convergence as well as a better knowledge of the isolation for the solutions. By setting the divided differences equal to zero the results can be used to solve equations with differentiable part too. © The Author(s), under exclusive licence to The Forum D’Analystes 2023.