Faculty Publications
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Item Extended local convergence for Newton-type solver under weak conditions(Babes-Bolyai University, 2021) Argyros, I.K.; George, S.; Senapati, K.We present the local convergence of a Newton-type solver for equations involving Banach space valued operators. The eighth order of convergence wasshown earlier in the special case of the k-dimensional Euclidean space, usinghypotheses up to the eighth derivative although these derivatives do not appearin the method. We show convergence using only the first derivative. This way weextend the applicability of the methods. Numerical examples are used to showthe convergence conditions. Finally, the basins of attraction of the method, onsome test problems are presented © 2021, Studia Universitatis Babes-Bolyai Mathematica. All Rights Reserved.Item 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.Item 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.