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<p>This study examines the convergence behaviour of a fourth-order Newton-type iterative method for approximating locally unique solutions of nonlinear systems in Banach spaces. Although the method employs only first-order derivative information, existing convergence analyses frequently require assumptions on higher-order derivatives, which restrict its practical applicability. To address this issue, we establish both local and semilocal convergence results using conditions formulated solely in terms of the first derivative. Numerical experiments are presented to validate and demonstrate the theoretical findings.</p>

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An improved two-step iterative method for solving systems of nonlinear equations

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Gopika Dinesh KC,
  • Ioannis K. Argyros,
  • Sreedeep Chekur Devadas

摘要

This study examines the convergence behaviour of a fourth-order Newton-type iterative method for approximating locally unique solutions of nonlinear systems in Banach spaces. Although the method employs only first-order derivative information, existing convergence analyses frequently require assumptions on higher-order derivatives, which restrict its practical applicability. To address this issue, we establish both local and semilocal convergence results using conditions formulated solely in terms of the first derivative. Numerical experiments are presented to validate and demonstrate the theoretical findings.