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

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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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Keywords

• Iterative method
• non-linear equation
• convergence analysis

MSC

•  65H04
•  65H05
•  65H20

References

• [1] N. Y. Abdul-Hassan, New predictor-corrector iterative methods with twelfth-order convergence for solving nonlinear equations, Amer. J. Appl. Math., 4 (2016), 175--180
  • View Article
  • Google Scholar


• [2] F. Ahmad, S. Hussain, S. Hussain, A. Rafiq, New twelfth order J-Halley method for solving nonlinear equations, Open Sci. J. Math. Appl., 1 (2013), 1--4
  • View Article
  • Google Scholar


• [3] A. S. Householder, The numerical treatment of a single nonlinear equation, McGraw-Hill, New York (1970)
  • View Article
  • MathSciNet


• [4] B. Kalantari, Method of creating graphical works based on polynomials, U.S. Patent, 6 (2005), 894--705
  • View Article
  • Google Scholar


• [5] S. Khattri, Another note on some quadrature based three-step iterative methods, Numer. Algebra, 3 (2013), 549--555
  • View Article
  • MathSciNet


• [6] B. Kong-ied, Two new eighth and twelfth order iterative methods for solving nonlinear equations, Int. J. Math. Comput. Sci., 16 (2021), 333--344
  • View Article
  • MathSciNet


• [7] S. Li, Fourth-order iterative method without calculating the higher derivatives for nonlinear equation, J. Algorithms Comput. Tech., 13 (2019), 8 pages
  • View Article
  • MathSciNet


• [8] X. Liu, X. Wang, A family of methods for solving nonlinear equations with twelfth-order convergence, Appl. Math., 4 (2013), 326--329
  • View Article
  • Google Scholar


• [9] N. A. Mir, T. Zaman, Some quadrature based three-step iterative methods for non-linear equations, Appl. Math. Comput., 193 (2007), 366--373
  • View Article
  • MathSciNet


• [10] M. S. K. Mylapalli, R. K. Palli, V. B. K. Vatti, An iterative method with twelfth order convergence for solving non-linear equations, Adv. Appl. Math. Sci., 20 (2021), 1633--1643
  • View Article
  • Google Scholar


• [11] A. Naseem, M. A. Rehman, T. Abdeljawad, Numerical algorithms for finding zeros of nonlinear equations and their dynamical aspects, J. Math., 2020 (2020), 11 pages
  • View Article
  • MathSciNet


• [12] M. Nawaz, A. Naseem, W. Nazeer, New twelfth order algorithms for solving nonlinear equations by using variational iteration technique, J. Prime Res. Math., 14 (2018), 24--36
  • View Article
  • MathSciNet


• [13] R. Thukral, New twelfth order iterative methods for finding multiple roots of nonlinear equations, Amer. J. Comput. Appl. Math., 5 (2015), 33--41
  • View Article


• [14] J. F. Traub, Iterative methods for solution of equations, Prentice-Hall, Englewood Cliffs (1964)
  • View Article
  • MathSciNet