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ABSTRACT <p>In this paper, we explore a double-step method for solving nonlinear equations containing differentiable and non-differentiable operators. Our approach is based on a combination of three different methods. We have analyzed the local convergence of the suggested method, considering both Lipschitz and L-average conditions, and established the superquadratic (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\approx 2.414\)</EquationSource> <EquationSource Format="MATHML"><math display="inline"> <mrow> <mo>≈</mo> <mn>2.414</mn> </mrow> </math></EquationSource> </InlineEquation>) order of convergence. Finally, we have pictured numerical results that are compared with those obtained by using several existing methods.</p>

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The Local Convergence of a Two-Step Combined Newton-Secant-Kurchatov Type Method under Two Different Continuity Conditions

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Charmita Pradhan,
  • Nishant Kumar,
  • J.P. Jaiswal

摘要

ABSTRACT

In this paper, we explore a double-step method for solving nonlinear equations containing differentiable and non-differentiable operators. Our approach is based on a combination of three different methods. We have analyzed the local convergence of the suggested method, considering both Lipschitz and L-average conditions, and established the superquadratic ( \(\approx 2.414\) ≈ 2.414 ) order of convergence. Finally, we have pictured numerical results that are compared with those obtained by using several existing methods.