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November 13, 2025Punjab University Journal of MathematicsOpen Access

Local convergence analysis of a three-step iterative scheme with Lagrangeinterpolation and basin of attraction

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Authors

MKMaira KhalidSASaima AkramMIMuhammad Ibrahim

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Overview

Local convergence analysis reveals improved stability and radius of convergence in nonlinear equations, suggesting effective initial guessing strategies.

Key Points

  • The method shows improved stability when applied to nonlinear equations and demonstrates larger radius of convergence.
  • A convergence region is established, along with error estimates, confirming solution uniqueness and reliability.
  • Analysis based on local convergence assesses dynamic behavior and convergence radius, highlighting effective performance.
  • The iterative scheme enhances numerical experimentation effectiveness, especially for transcendental equations with fewer chaotic behaviors.

Cite This Study

Khalid et al. (2025) studied this question.

synapsesocial.com/papers/692523cec0ce034ddc3551cdhttps://doi.org/10.52280/pujm.2025.57(05)03
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