A stable optimal solver for nonlinear equations with semilocal convergence using majorizing sequences in banach spaces

• Sania Qureshi ^[1] ; Ioannis K. Argyros ^[2] ; Higinio Ramos ^[3] ; Amanullah Soomro ^[1] ; Paras Nizamani ^[1] ; G Thangkhenpau ^[4] ; Sunil Panday ^[4]
  1. [1] Department of Basic Sciences and Related Studies, Mehran University of Engineering & Technology
  2. [2] Department of Computing and Mathematics Sciences, Cameron University
  3. [3] Scientific Computing Group, Universidad de Salamanca
  4. [4] Department of Mathematics, National Institute of Technology Manipur, Imphal

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• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 83, Nº. 3, 2026, págs. 515-549
• Idioma: inglés
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• Resumen

  • In this work, we present a novel optimal iterative solver that is highly effective and accurate, achieving fourth-order convergence. The proposed method adheres to the Kung–Traub conjecture, with an efficiency index of 1.5874. The solver utilizes a combination of local and semi-local analyses to improve its runtime and rate of convergence. The basins of attraction are drawn to investigate stability and to illustrate the implementation of the optimal fourth-order numerical root-solver for solving nonlinear systems. Numerical experiments demonstrate the versatility of the solver across various mathematical contexts, including polynomiography, and show superior performance compared to several existing optimal solvers. Application problems from different scientific fields, such as kinetics, heat transfer, neurophysiology, and particle physics, are numerically solved to further demonstrate the potential of the proposed optimal solver.