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<p>The aim of this work is twofold: first, to develop a memory-based Kurchatov conformable iterative method to solve nonlinear equations; second, to provide a convergence sphere for global visualization of real dynamics. We establish the R-order of convergence for the proposed method and demonstrate how the convergence sphere maps initial guesses onto a closed surface, allowing for a compact analysis of global stability and basin connectivity. Moreover, this study investigates the root convergence trajectory, the dynamic behavior of the method, numerical results, and the concept of Approximated Order of Convergence (<i>ACOC</i>), all of which support and strengthen the theoretical results.</p>

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Convergence sphere of R-order conformable Kurchatov method with memory

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Sapan Kumar Nayak

摘要

The aim of this work is twofold: first, to develop a memory-based Kurchatov conformable iterative method to solve nonlinear equations; second, to provide a convergence sphere for global visualization of real dynamics. We establish the R-order of convergence for the proposed method and demonstrate how the convergence sphere maps initial guesses onto a closed surface, allowing for a compact analysis of global stability and basin connectivity. Moreover, this study investigates the root convergence trajectory, the dynamic behavior of the method, numerical results, and the concept of Approximated Order of Convergence (ACOC), all of which support and strengthen the theoretical results.