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Analysis of institutional authors

Chicharro, Francisco IAuthor

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November 3, 2024
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A modified two-step optimal iterative method for solving nonlinear models in one and higher dimensions

Publicated to: MATHEMATICS AND COMPUTERS IN SIMULATION. 229 448-467 - 2025-01-01 229(), DOI: 10.1016/j.matcom.2024.09.021

Authors:

Chang, Chih-Wen; Qureshi, Sania; Argyros, Ioannis K.; Chicharro, Francisco I.; Soomro, Amanullah
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Affiliations

Cameron Univ, Dept Comp & Math Sci, Lawton, OK 73505 USA - Author
Lebanese Amer Univ, Dept Comp Sci & Math, POB 13-5053, Beirut, Lebanon - Author
Mehran Univ Engn & Technol, Dept Basic Sci & Related Studies, Jamshoro 76062, Pakistan - Author
Natl United Univ, Dept Mech Engn, Miaoli, Taiwan - Author
Near East Univ, Dept Math, TR-99138 Mersin, Turkiye - Author
Univ Politecn Valencia, Inst Univ Matemat Multidisciplinar, Valencia 46022, Spain - Author
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Abstract

Iterative methods are essential tools in computational science, particularly for addressing nonlinear models. This study introduces a novel two-step optimal iterative root-finding method designed to solve nonlinear equations and systems of nonlinear equations. The proposed method exhibits the optimal convergence, adhering to the Kung-Traub conjecture, and necessitates only three function evaluations per iteration to achieve a fourth-order optimal iterative process. The development of this method involves the amalgamation of two well-established third-order iterative techniques. Comprehensive local and semilocal convergence analyses are conducted, accompanied by a stability investigation of the proposed approach. This method marks a substantial enhancement over existing optimal iterative methods, as evidenced by its performance in various nonlinear models. Extensive testing demonstrates that the proposed method consistently yields accurate and efficient results, surpassing existing algorithms in both speed and accuracy. Numerical simulations, including real-world models such as boundary value problems and integral equations, indicate that the proposed optimal method outperforms several contemporary optimal iterative techniques.
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Keywords

Computational cosComputational costComputational order of convergenceConvergenceEfficiency indexEquationsFamilIterative algorithmsNonlinear modelsRoot-finding methodsSchemes

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal MATHEMATICS AND COMPUTERS IN SIMULATION due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2025, it was in position 3/344, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2026-04-08:

  • WoS: 12
  • Scopus: 12
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Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2026-04-08:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 4.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 4 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 2.
  • The number of mentions on the social network X (formerly Twitter): 2 (Altmetric).
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Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Cyprus; Lebanon; Pakistan; Taiwan; Turkey; United States of America.

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