Comparative Analysis of Fixetpoint and Halley Methods For Numerically Solving The Roots of Non-Linear Equations

Laela Safitri, Syaharuddin Syaharuddin

Abstract


Abstract: This study aims to analyze the comparison of Fixetpoint and Halley methods in numerically solving the roots of non-linear equations. The assessment criteria to be used include convergence, stability, and computational speed of each method. The equations used include trigonometric, pilinomial, exponential and logarithmic. Experiments were conducted 8 times with an error of 0.001 and using a maximum of 100 iterations. Of the four cases of solving the tested equations, the fixetpoint method is faster than the halley method with 5 iterations on trigonometric equations. In polynomial equations the fixetpoint method is faster than newton rapshon with 100 iterations. in exponential equations the fixetpoint method is faster than hallley with 1 iteration. In the logarithmic equation the fixetpoint method is slower than the halley method with 14 iterations, therefore it can be said that the fixtpoint method has a faster convergence rate and higher accuracy than the Halley method in most cases. So it can be said that Fixetpoint is the best method in solving the roots of non-linear equations. These findings provide new insights in choosing the right method for numerical applications in solving the roots of non-linear equations, and contribute to the development of more efficient numerical algorithms.

 


Keywords


Fixed-point method, Halley's method, roots of non-linear equations, numerical solution, convergence, and comparative analysis.

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References


Apriano, L., & Rizal, Y. (2024). Application of the Inflection Point in the Evaluation of the Halley and Newton-Raphson Techniques for Finding the Root of Non-Linear Equations. Mathematical Journal of Modeling and Forecasting, 2(1), 27-31. https://doi.org/10.24036/mjmf.v2i1.23 https://doi.org/10.24036/mjmf.v2i1.23

Arianto, T., Wahyuni, H. I., & Kurnianto, E. (2019). Growth Parameter Analysis of the Second Generation of Red and Black Cockerels at the Center for Breeding and Cultivation of Non-Ruminant Livestock Satker Maron Chicken in Temanggung Regency. Indonesian Journal of Animal Science, 21(1), 10. https://doi.org/10.25077/jpi.21.1.10-17.2019 https://doi.org/10.25077/jpi.21.1.10-17.2019

Azmi, A. U., Hidayat, R., & Arif, M. Z. (2019). Comparison of Particle Swarm Optimization (Pso) and Glowworm Swarm Optimization (Gso) Algorithms in Solving Nonlinear Equation Systems. Scientific Magazine of Mathematics and Statistics, 19(1), 29. https://doi.org/10.19184/mims.v19i1.17263 https://doi.org/10.19184/mims.v19i1.17263

Hayu, G. A., Mifta, A., & A., S. (2020). Comparative Analysis of Capacity of Steel-Concrete Composite Beams with Steel Headed Stud and UNP Stud. Berkala Sainstek, 8(4), 140. https://doi.org/10.19184/bst.v8i4.18621 https://doi.org/10.19184/bst.v8i4.18621Hutagalung, S. N. (2017). Understanding Numerical Methods (Case Study of New-Rhapson Method) Using Matlab Programmer. Journal of Information Technology, 1(1), 95. https://doi.org/10.36294/jurti.v1i1.109 https://doi.org/10.36294/jurti.v1i1.109

Jumawanti, I., Sutrisno, S., & Surarso, B. (2018). Comparison Results of Improved Newton-Raphson Method Based on Adomian Decomposition and Some Classical Methods on Non-Linear Equation Problems. Journal of Fundamental Mathematics and Applications (JFMA), 1(1), 39. https://doi.org/10.14710/jfma.v1i1.8 https://doi.org/10.14710/jfma.v1i1.8

Mandailina, V., Pramita, D., Ibrahim, M., Ratu Perwira Negara, H., & History, A. (2020). http://ejournal.radenintan.ac.id/index.php/desimal/index Wilkinson Polynomials: Accuracy Analysis Based on Numerical Methods of the Taylor Series Derivative ARTICLE INFO ABSTRACT. Decimal: Journal of Mathematics, 3(2), 155-160. https://doi.org/10.24042/djm https://doi.org/10.24042/djm.v3i2.6134

Pandia, W., & Sitepu, I. (2021). Determination of Roots of Nonlinear Equations by Numerical Methods. Journal of Mutiara Pendidikan Indonesia, 6(2), 122-129. https://doi.org/10.51544/mutiarapendidik.v6i2.2326 https://doi.org/10.51544/mutiarapendidik.v6i2.2326

Ritonga, J., & Suryana, D. (2019). Comparison of Convergence Speed of Nonlinear Equation Root Fixed Point Method with Newton Raphson Method Using Matlab. INFORMASI (Journal of Informatics and Information Systems), 11(2), 51-64. https://doi.org/10.37424/informasi.v11i2.17 https://doi.org/10.37424/informasi.v11i2.17

Safitri, N., & Lahallo, F. F. (2024). Profit Planning Analysis through Break Even Point (BEP) Calculation at Mama Mila's Pinang Business in Remu Market, Sorong City, Southwest Papua. Journal of Jendela Ilmu, 5(1), 1-6. https://doi.org/10.34124/ji.v5i1.163 https://doi.org/10.34124/ji.v5i1.163

Vilinea, A. R., Rusyaman, E., & Djauhari, E. (2020). Solution of Non-Linear Fractional Differential Equations Using Telescoping Decomposition Method. Journal of Integrative Mathematics, 15(2), 139. https://doi.org/10.24198/jmi.v15i2.23376 https://doi.org/10.33379/gtech.v1i1.262


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