A New Sixth Order Iterative Method with Three Step for Solving Nonlinear Equation

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Published: Dec 30, 2023
Keywords:
Nonlinear equations iterative method Order of convergence

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Somsiri Payakkarak
Education Program in Mathematics, Faculty of Education, Suratthani Rajabhat University
Thitirat Chante
Department of Mathematics, Faculty of Science, Mahasarakham University
Athittaya Kaewpikul
Department of Mathematics, Faculty of Science, Mahasarakham University
Butsakorn Kong-ied
Department of Mathematics, Faculty of Science, Mahasarakham University

Abstract

This paper presented a new three-step iterative method, free from second derivative for solving nonlinear equation. The idea was derived from the two third-order convergent iterative methods, namely Halley's method and Sharma's method. These were integrated to enhance the Classical Chebyshev method, which also possessed third-order convergence. Moreover, an analysis of the convergence order for this new iterative method was considered and demonstrated sixth-order convergence. Additionally, a numerical example was provided to show the efficiency of this new iterative method.

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How to Cite
Payakkarak, S., Chante, T., Kaewpikul, A., & Kong-ied, B. (2023). A New Sixth Order Iterative Method with Three Step for Solving Nonlinear Equation. Journal of Science Ladkrabang, 32(2), 113–121. Retrieved from https://li01.tci-thaijo.org/index.php/science_kmitl/article/view/254706
Issue
Vol. 32 No. 2 (2023): July - December 2023
Section
Academic article
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

References

Behl, R. and Kanwar, V. 2013. Variants of Chebyshev's Method with Optimal Order of Convergence. Tamsui Oxford Jor I of Information and Mathematical Sciences, 29(1), 39-53.

Ezquerro, A., Hermandez, M.A. 2003. A Uniparametric Halley-type iteration with free second deritive. Int. J. Pure Appl. Math, 6, 99-110.

Sharma, J.R. 2005. A composite third-order Newton Steffensen method for solving nonlinear equations. Appl. Math. Comput, 169, 242-246.

Sabri, R.I. 2015. A New Three Step Iterative Method without Second Derivative for Solving Nonlinear Equations. Baghdad Science Journal, 12(3), 632-637.

Chun, C., Lee, M.Y., Neta, B. and Dzunic, J. 2012. On optimal fourth-order iterative methods free from second derivative and their dynamics. Ap-plied Mathematics and Computation, 218, 6427- 6438.

Hueso, J.L., Martinez, E. and Torregrosa, J.R. 2009. Third and fourth order iterative methods free from second derivative for nonlinear systems. Applied Mathematics and Computation, 190-197.

Purnama, E.L., Imran, M. and Leli, D. 2016. A sixth-order derivative-free iterative method for solving nonlinear equation, Bulletin of Mathematics, 1, 1-8.

Han, J., He, H., Xu, A. and Cen, Z. 2010. A second derivative free variant of Halley’s method with sixth order convergence. Journal of Pure and Applied Mathematics: Advances and Applications, 3, 195-203.

Kumar, S.M. 2009. A Six-order Variants of Newton's Method for Solving Nonlinear Equations. Computational Methods In Science and Technology, 15(2), 185-193.