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<p>In this study, a three-step iterative technique with fifth-order convergence is investigated to solve the systems of nonlinear equations. The primary goal is to maximize the convergence order and computational efficiency. To support the findings, efficiency index is calculated and compared with that of existing techniques. This factor is extensively investigated through theoretical and numerical approaches. Performance and stability are demonstrated by conducting numerical tests on various nonlinear problems. Numerical experimentation demonstrates high degree of precision and efficiency of the method.</p>

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Solution of nonlinear problems: A simple yet efficient weighted-Newton approach

  • 期刊论文

  • 发表日期：

    2025年9月11日

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  • Harmandeep Singh,
  • Janak Raj Sharma,
  • Sunil Kumar

摘要

In this study, a three-step iterative technique with fifth-order convergence is investigated to solve the systems of nonlinear equations. The primary goal is to maximize the convergence order and computational efficiency. To support the findings, efficiency index is calculated and compared with that of existing techniques. This factor is extensively investigated through theoretical and numerical approaches. Performance and stability are demonstrated by conducting numerical tests on various nonlinear problems. Numerical experimentation demonstrates high degree of precision and efficiency of the method.