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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 2, Pages 214–221
(Mi zvmmf9650)
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This article is cited in 9 scientific papers (total in 9 papers)
On novel classes of iterative methods for solving nonlinear equations
F. Soleymania, B. S. Mousavib a Department of Math. Islamic Azad Univ., Zahedan Branch, Zahedan, Iran
b Young Researchers Club, Islamic Azad Univ., Zahedan Branch, Zahedan, Iran
Abstract:
In this paper, we establish two new classes of derivative-involved methods for solving single valued nonlinear equations of the form $f(x)=0$. The first contributed two-step class includes two evaluations of the function and one of its first derivative where its error analysis shows a fourth-order convergence. Next, we construct a three-step high-order class of methods including four evaluations per full cycle to achieve the seventh order of convergence. Numerical examples are included to re-verify the theoretical results and moreover put on show the efficiency of the new methods from our classes.
Key words:
nonlinear equations, weight function, simple root, efficiency index, order of convergence,
multi-point methods.
Received: 16.06.2011
Citation:
F. Soleymani, B. S. Mousavi, “On novel classes of iterative methods for solving nonlinear equations”, Zh. Vychisl. Mat. Mat. Fiz., 52:2 (2012), 214–221; Comput. Math. Math. Phys., 52:2 (2012), 203–210
Linking options:
https://www.mathnet.ru/eng/zvmmf9650 https://www.mathnet.ru/eng/zvmmf/v52/i2/p214
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Abstract page: | 316 | Full-text PDF : | 117 | References: | 66 | First page: | 11 |
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