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August 26, 2025Open Access

Efficient Higher-Order Iterative Schemes for Enhanced Convergence and Dynamical Analysis in Real-World Applications.

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Authors

MRMuhammad RazaMHMashood Ul haqDTDaanish Toheed

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Overview

New fourth to seventh-order iterative schemes improve convergence in nonlinear problems, indicating broader applications.

Key Points

  • The proposed schemes demonstrate improved convergence compared to existing methods, enhancing their applicability.
  • The basin of attraction indicates that our schemes generate larger regions than previous iterations, promoting their efficiency.
  • The convergence order of the methods is confirmed theoretically while showcasing good computational performance in real-world analyses.
  • Applications span across fields including blood rheology, fluid mechanics, and quantum mechanics, emphasizing their broad relevance.

Cite This Study

Raza et al. (2025) studied this question.

synapsesocial.com/papers/68af63efad7bf08b1eae4b1ehttps://doi.org/10.21203/rs.3.rs-7439311/v1
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Also Consider

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  2. 2Optimizing Nonlinear Problem Solving: Novel Third to Eighth-Order Iterative Schemes via Homotopy Perturbation Method2025
  3. 3A Class of Sixth-Order Iterative Methods for Solving Nonlinear Systems: The Convergence and Fractals of Attractive Basins2024 · 3 citations
  4. 4Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results2024 · 8 citations
  5. 5On memory-based higher-order iterative schemes for nonlinear equations: complex dynamics and applications2025