An optimal fourth order method for solving nonlinear equations
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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.
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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
- Nonlinear equations
- basins of attraction
- iterative methods
- optimal methods
- complex dynamics
MSC
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