ENHANCING NONLINEAR EQUATION SOLUTIONS THROUGH THE COMBINATION OF VARIANT NEWTON’S AND HALLEY’S METHODS

Authors

  • Kazhal Mohammed Ali Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistan Region,
  • Bayda Gh. Fathi Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistan Region, Iraq

DOI:

https://doi.org/10.25271/sjuoz.2025.13.4.1594

Keywords:

Newton’s method, Variant of Newton’s method, Halley’s method, Efficiency index, Nonlinear equations

Abstract

This work presents a new iterative method for solving single-variable nonlinear equations. The method achieves ninth-order convergence with just three derivative evaluations per step, offering both accuracy and lower computational cost. Unlike slower bracketing methods, it builds on faster open methods, though these may sometimes fail to converge. By blending ideas from Newton's and Halley's methods, the new approach provides strong performance, as shown by a detailed convergence analysis and MATLAB tests. Compared to existing techniques, it finds solutions in fewer steps and less time, making it especially effective for difficult nonlinear problems

      

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Author Biography

Bayda Gh. Fathi, Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistan Region, Iraq

Department of Mathematics, College of Science, University of Zakho, Zakho, Kurdistan Region, Iraq

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Published

2025-10-08

How to Cite

Mohammed Ali, K., & Fathi, B. (2025). ENHANCING NONLINEAR EQUATION SOLUTIONS THROUGH THE COMBINATION OF VARIANT NEWTON’S AND HALLEY’S METHODS. Science Journal of University of Zakho, 13(4), 589–598. https://doi.org/10.25271/sjuoz.2025.13.4.1594

Issue

Vol. 13 No. 4 (2025): October-December issue

Section

Science Journal of University of Zakho

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Copyright (c) 2025 Kazhal Mohammed Ali, Bayda Gh. Fathi

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