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 Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 4, Pages 555–561 (Mi zvmmf9224)

On derivative free cubic convergence iterative methods for solving nonlinear equations

M. Dehghana, M. Hajarianab

a Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914
b Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, G.C., Evin, Teheran 19839, Iran

Abstract: Finding the zeros of a nonlinear equation is a classical problem of numerical analysis which has various applications in many science and engineering. In this problem we seek methods that lead to approximate solutions. Sometimes the applications of the iterative methods depended on derivatives are restricted in Physics, chemistry and engineering. In this paper, we propose two iterative formulas without derivatives. These methods are based on the central-difference and forward-difference approximations to derivatives. The convergence analysis shows that the methods are cubically and quadratically convergent respectively. The best property of these schemes are that they are derivative free. Several numerical examples are given to illustrate the efficiency and performance of the proposed methods.

Key words: Newton's theorem, Newton's method, cubic convergence, divided differences, nonlinear equation, iterative method.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:4, 513–519

Bibliographic databases:

UDC: 519.615.5
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Citation: M. Dehghan, M. Hajarian, “On derivative free cubic convergence iterative methods for solving nonlinear equations”, Zh. Vychisl. Mat. Mat. Fiz., 51:4 (2011), 555–561; Comput. Math. Math. Phys., 51:4 (2011), 513–519

Citation in format AMSBIB
\Bibitem{DehHaj11} \by M.~Dehghan, M.~Hajarian \paper On derivative free cubic convergence iterative methods for solving nonlinear equations \jour Zh. Vychisl. Mat. Mat. Fiz. \yr 2011 \vol 51 \issue 4 \pages 555--561 \mathnet{http://mi.mathnet.ru/zvmmf9224} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2858620} \transl \jour Comput. Math. Math. Phys. \yr 2011 \vol 51 \issue 4 \pages 513--519 \crossref{https://doi.org/10.1134/S0965542511040051} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000290035800002} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955623487} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Dehghan M., Hajarian M., “Fourth-order variants of Newton's method without second derivatives for solving non-linear equations”, Eng. Comput., 29:3-4 (2012), 356–365
2. Amat S., Argyros I.K., Busquier S., Alberto Magrenan A., “Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions”, Numer. Algorithms, 74:2 (2017), 371–391
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