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

Main Article Content

Somsiri Payakkarak
Thitirat Chante
Athittaya Kaewpikul
Butsakorn Kong-ied


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.

Article Details

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
Academic article


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.