On the construction of three step derivative free four-parametric methods with accelerated order of convergence
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Authors
Fiza Zafar
- Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
Saima Akram
- Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
Nusrat Yasmin
- Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
Moin-ud-Din Junjua
- Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
Abstract
In this paper, a general procedure to develop some four-parametric with-memory methods to find simple
roots of nonlinear equations is proposed. The new methods are improved extensions of with derivative with-
out memory iterative methods. We used four self-accelerating parameters to boost up the convergence order
and computational efficiency of the proposed methods without using any additional function evaluations.
Numerical examples are presented to support the theoretical results of the methods. We further investigate
the dynamics of the methods in the complex plane.
Share and Cite
ISRP Style
Fiza Zafar, Saima Akram, Nusrat Yasmin, Moin-ud-Din Junjua, On the construction of three step derivative free four-parametric methods with accelerated order of convergence, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4542--4553
AMA Style
Zafar Fiza, Akram Saima, Yasmin Nusrat, Junjua Moin-ud-Din, On the construction of three step derivative free four-parametric methods with accelerated order of convergence. J. Nonlinear Sci. Appl. (2016); 9(6):4542--4553
Chicago/Turabian Style
Zafar, Fiza, Akram, Saima, Yasmin, Nusrat, Junjua, Moin-ud-Din. "On the construction of three step derivative free four-parametric methods with accelerated order of convergence." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4542--4553
Keywords
- Root finding
- four-parametric
- accelerated order of convergence
- derivative free.
MSC
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