PENYELESAIAN PERSAMAAN NON LINEAR MENGGUNAKAN METODE ITERASI TIGA LANGKAH

Nafisha Huang - Padang State University
Yusmet Rizal - padang state university

Abstract


The Three-Step Iterative Method is a multistep approach designed to determine the roots of complex non-linear equations. Developed using Taylor Series, Quadratic Equations, and Hermite Interpolation, this method provides an alternative for solving complicated equations numerically and analytically. This study aims to examine the formulation of the method, design an algorithm in a flowchart, and analyze its convergence order. The research adopts a literature review methodology by conducting an in-depth analysis of relevant references. The algorithm's implementation is tested through computer programming to evaluate its numerical effectiveness. The results demonstrate that the method achieves high-order convergence, enabling faster solutions with minimal error. In conclusion, the Three-Step Iterative Method is an efficient and accurate solution for resolving complex non-linear equations.

Full Text:

PDF

References


R. Munir, Metode Numerik, Lima. Bandung: Informatika Bandung, 2021.

D. V. Griffiths and I. M. Smith, Numerical Methods for Engineers. McGraw-Hill Science/Engineering/Math, 2006. doi: 10.1201/9781420010244.

R. Thukral and M. S. Petković, “A family of three-point methods of optimal order for solving nonlinear equations,” J. Comput. Appl. Math., vol. 233, no. 9, pp. 2278–2284, 2010, doi: 10.1016/j.cam.2009.10.012.

S. Yaseen, F. Zafar, and F. I. Chicharro, “A Seventh Order Family of Jarratt Type Iterative Method for Electrical Power Systems,” Fractal Fract., vol. 7, no. 4, pp. 1–16, 2023, doi: 10.3390/fractalfract7040317.

M. S. K. Mylapalli, R. K. Palli, and R. Sri, “A ninth order iterative method for solving non-linear equations with high-efficiency index,” Adv. Math. Sci. J., vol. 9, no. 7, pp. 5283–5290, 2020, doi: 10.37418/amsj.9.7.97.

M. Nazir, Metode Penelitian. Jakarta: Galia Indonesia, 2014.

S. Hanzely, D. Kamzolov, D. Pasechnyuk, A. Gasnikov, P. Richtárik, and M. Takáč, “A Damped Newton Method Achieves Global O(1/K2) and Local Quadratic Convergence Rate,” Adv. Neural Inf. Process. Syst., vol. 35, no. NeurIPS, pp. 1–15, 2022.

W. Zhou, X. Wei, L. Wang, and G. Wu, “A superlinear iteration method for calculation of finite length journal bearing’s static equilibrium position,” R. Soc. Open Sci., vol. 4, no. 5, 2017, doi: 10.1098/rsos.161059.




DOI: http://dx.doi.org/10.24036/unpjomath.v10i1.17052