Browsing by Author "Saeed, M."

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    An apriori parameter choice strategy and a fifth order iterative scheme for Lavrentiev regularization method
    (Institute for Ionics, 2023) George, S.; Saeed, M.; Argyros, I.K.; Padikkal, J.
    In this paper, we propose a new source condition and introduce a new apriori parameter choice strategy for Lavrentiev regularization method for nonlinear ill-posed operator equation involving a monotone operator in the setting of a Hilbert space. Also, a fifth order iterative method is being proposed for approximately solving Lavrentiev regularized equation. A numerical example is illustrated to demonstrate the performance of the method. © 2022, The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics.
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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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    Extending the Applicability of Cordero Type Iterative Method
    (MDPI, 2022) Remesh, K.; Argyros, I.K.; Saeed, M.; George, S.; Padikkal, J.
    Symmetries play a vital role in the study of physical systems. For example, microworld and quantum physics problems are modeled on the principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Most of these studies reduce to solving nonlinear equations in suitable abstract spaces iteratively. In particular, the convergence of a sixth-order Cordero type iterative method for solving nonlinear equations was studied using Taylor expansion and assumptions on the derivatives of order up to six. In this study, we obtained order of convergence six for Cordero type method using assumptions only on the first derivative. Moreover, we modified Cordero’s method and obtained an eighth-order iterative scheme. Further, we considered analogous iterative methods to solve an ill-posed problem in a Hilbert space setting. © 2022 by the authors.
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    On Newton’s Midpoint-Type Iterative Scheme’s Convergence
    (Springer, 2022) Krishnendu, R.; Saeed, M.; George, S.; Padikkal, J.
    This paper introduce new three step iterative schemes with order of convergence five and six for solving nonlinear equations in Banach spaces. The proposed scheme’s convergence is assessed using assumptions on the operator’s derivatives up to order two. Unlike earlier studies, the convergence study of these methods are not based on the Taylor’s expansion. Numerical examples and Basin of attractions are given in this study © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.