Research Article

Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox

Volume: 14 Number: 2 June 27, 2025
EN

Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox

Abstract

In this study, the results obtained by using the Red Fox method, a new metaheuristic optimization method, and the Newton Raphson method, which is one of the numerical methods, in finding the solutions of nonlinear systems of equations, are compared and these comparative analyses are evaluated and recommendations are presented.

Keywords

References

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  3. Gower R, Lorenz DA, Winkler M. A Bregman–Kaczmarz method for nonlinear systems of equations. Comput Optim Appl. 2023;87(3):1059–1098.
  4. Pourrajabian A, Ebrahimi R, Mirzaei M, Shams M. Applying genetic algorithms for solving nonlinear algebraic equations. Appl Math Comput. 2013;219(24):11483–11494.
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  6. Odan S. Metaheuristic method for solving systems of equations. arXiv. 2024. Available from: https://arxiv.org/abs/2409.16958
  7. Verma P, Parouha RP. Solving systems of nonlinear equations using an innovative hybrid algorithm. Iranian J Sci Technol Trans Electr Eng. 2022; 46:1005–1027.
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Details

Primary Language

English

Subjects

Algebraic Structures in Mathematical Physics, Mathematical Physics (Other)

Journal Section

Research Article

Publication Date

June 27, 2025

Submission Date

October 20, 2024

Acceptance Date

February 27, 2025

Published in Issue

Year 2025 Volume: 14 Number: 2

APA
Köse, B., Demirtürk, B., & Konca, Ş. (2025). Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox. Turkish Journal of Nature and Science, 14(2), 1-10. https://doi.org/10.46810/tdfd.1570735
AMA
1.Köse B, Demirtürk B, Konca Ş. Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox. TJNS. 2025;14(2):1-10. doi:10.46810/tdfd.1570735
Chicago
Köse, Bayram, Bahar Demirtürk, and Şükran Konca. 2025. “Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox”. Turkish Journal of Nature and Science 14 (2): 1-10. https://doi.org/10.46810/tdfd.1570735.
EndNote
Köse B, Demirtürk B, Konca Ş (June 1, 2025) Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox. Turkish Journal of Nature and Science 14 2 1–10.
IEEE
[1]B. Köse, B. Demirtürk, and Ş. Konca, “Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox”, TJNS, vol. 14, no. 2, pp. 1–10, June 2025, doi: 10.46810/tdfd.1570735.
ISNAD
Köse, Bayram - Demirtürk, Bahar - Konca, Şükran. “Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox”. Turkish Journal of Nature and Science 14/2 (June 1, 2025): 1-10. https://doi.org/10.46810/tdfd.1570735.
JAMA
1.Köse B, Demirtürk B, Konca Ş. Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox. TJNS. 2025;14:1–10.
MLA
Köse, Bayram, et al. “Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox”. Turkish Journal of Nature and Science, vol. 14, no. 2, June 2025, pp. 1-10, doi:10.46810/tdfd.1570735.
Vancouver
1.Bayram Köse, Bahar Demirtürk, Şükran Konca. Two Approaches For Solving Nonlinear Equation Systems: Newton Raphson and Red Fox. TJNS. 2025 Jun. 1;14(2):1-10. doi:10.46810/tdfd.1570735