New twelfth order iterative method for solving nonlinear equations and their dynamical aspects

Volume 28, Issue 1, pp 52--59 http://dx.doi.org/10.22436/jmcs.028.01.05
Publication Date: May 02, 2022 Submission Date: September 30, 2021 Revision Date: March 11, 2022 Accteptance Date: March 18, 2022

Authors

P. Janngam - Department of Mathematics, Faculty of Education, Buriram Rajabhat University, Buriram, Thailand. C. Comemuang - Department of Mathematics, Faculty of Science, Buriram Rajabhat University, Buriram, Thailand.


Abstract

The aims of this paper are to present new twelfth order iterative methods for solving nonlinear equations and one of them is second derivative free which has been removed using the interpolation technique. Analysis of convergence finalized that the order of convergence is twelfth. Some numerical examples illustrate that the algorithm is more efficient and performs better than other methods with the same order. In the end, we present the basins of attraction using some complex polynomials of different degrees to observe the fractal behavior and dynamical aspects of the proposed algorithms.


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ISRP Style

P. Janngam, C. Comemuang, New twelfth order iterative method for solving nonlinear equations and their dynamical aspects, Journal of Mathematics and Computer Science, 28 (2023), no. 1, 52--59

AMA Style

Janngam P., Comemuang C., New twelfth order iterative method for solving nonlinear equations and their dynamical aspects. J Math Comput SCI-JM. (2023); 28(1):52--59

Chicago/Turabian Style

Janngam, P., Comemuang, C.. "New twelfth order iterative method for solving nonlinear equations and their dynamical aspects." Journal of Mathematics and Computer Science, 28, no. 1 (2023): 52--59


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