An optimal fourth order method for solving nonlinear equations

Volume 23, Issue 2, pp 86--97 http://dx.doi.org/10.22436/jmcs.023.02.02
Publication Date: October 09, 2020 Submission Date: June 29, 2020 Revision Date: July 16, 2020 Accteptance Date: August 03, 2020

Authors

M. A. Hafiz - Department of Mathematics, Faculty of Science and Arts, Najran University, Najran 1988, Saudi Arabia. M. Q. Khirallah - Department of Mathematics, Faculty of Science and Arts, Najran University, Najran 1988, Saudi Arabia. - Department of Mathematics and Computer Science, Faculty of Science, Ibb University, Yemen.


Abstract

In this paper, we use both weight functions and composition techniques together for solving non-linear equations. We designed a new fourth order iterative method to increase the order of convergence without increasing the functional evaluations in a drastic way. This method uses one evaluation of the function and two evaluations of the first derivative. The new method attains the optimality with efficiency index 1.587. The convergence analysis of our new methods is discussed. Furthermore, the correlations between the attracting domains and the corresponding required number of iterations have also been illustrated and discussed. The comparison with several numerical methods and the use of complex dynamics and basins of attraction show that the new method gives good results.


Share and Cite

  • Share on Facebook
  • Share on Twitter
  • Share on LinkedIn
ISRP Style

M. A. Hafiz, M. Q. Khirallah, An optimal fourth order method for solving nonlinear equations, Journal of Mathematics and Computer Science, 23 (2021), no. 2, 86--97

AMA Style

Hafiz M. A., Khirallah M. Q., An optimal fourth order method for solving nonlinear equations. J Math Comput SCI-JM. (2021); 23(2):86--97

Chicago/Turabian Style

Hafiz, M. A., Khirallah, M. Q.. "An optimal fourth order method for solving nonlinear equations." Journal of Mathematics and Computer Science, 23, no. 2 (2021): 86--97


Keywords


MSC


References