Existing methods have limitations in terms of convergence order and computational cost

The gap

Evidence profile

Sourced from the stated research gap of the source papers, classified as general, spanning 3 journals.

Supporting evidence — 3 representative gaps

• A New Three-Step Modification of a Fifth-Order Iterative Method with Weight Functions for Solving Nonlinear Equations (2026) · World Scientific News · doi

  Existing methods have limitations in terms of convergence order and computational cost. There is a need for more efficient and competitive methods for solving nonlinear equations.

  generalstated research gapevidence 5/5
  Keywords: existing methods have limitations terms convergence order computational
• Simultaneous determination of multiple zeros via Schröder–Ehrlich-type corrections (2026) · Numerical Algorithms · doi

  Standard iterative methods often exhibit a significant loss of order of convergence when applied to problems involving multiple roots. There is a need for numerical procedures specifically designed for the simultaneous approximation of multiple roots of nonlinear equations.

  generalstated research gapevidence 5/5
  Keywords: standard iterative methods often exhibit significant loss order
• Computational Mathematics and Numerical Techniques (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi

  The paper identifies the need for efficient and reliable methods for computing the roots of non-linear scalar equations. The paper notes that existing methods may have limitations, such as slow convergence or requiring the computation of derivatives.

  generalstated research gapevidence 5/5
  Keywords: paper identifies need efficient reliable methods computing roots

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