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The paper asserts to build higher-order iterative methods for solving nonlinear equations. These schemes utilize with-memory techniques and incorporate approximations of self-accelerating parameters. The enumeration of this parameter is achieved through the use of Hermite interpolating polynomials to advance the convergence rate of the without-memory scheme from 8 to 9.5826, 9.7958, and 10 without requiring any additional function evaluations. Computational results confirm that the newly proposed schemes are efficient and preferable compared to existing methods.

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Three Efficient Memory-Based Iterative Methods for Finding Roots of Nonlinear Equations

  • 会议论文

  • 发表日期：

    2025年

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  • Ekta Sharma,
  • Sunil Panday,
  • Shubham Kumar Mittal,
  • Bhavna Panday

摘要

The paper asserts to build higher-order iterative methods for solving nonlinear equations. These schemes utilize with-memory techniques and incorporate approximations of self-accelerating parameters. The enumeration of this parameter is achieved through the use of Hermite interpolating polynomials to advance the convergence rate of the without-memory scheme from 8 to 9.5826, 9.7958, and 10 without requiring any additional function evaluations. Computational results confirm that the newly proposed schemes are efficient and preferable compared to existing methods.