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A class of efficient derivative free iterative method with and without memory for solving nonlinear equations

    Author

    • Raziyeh Erfanifar

    Faculty of Mathematics and Statistics, Malayer University, Malayer, Iran.

,

Document Type : Regular paper

10.52547/CMCMA.1.2.20
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Abstract

In the present paper, at first, we propose a new two-step iterative method for solving nonlinear equations. This scheme is based on the Steffensen's method, in which the order of convergence is four. This iterative method requires only three functions evaluation in each iteration, therefore it is optimal in the sense of the Kung and Traub conjecture. Then we extend it to the method with memory, which the order of convergence is six. Finally, numerical examples indicate that the
obtained methods in terms of accuracy and computational cost are superior to the
famous forth-order methods.

Keywords

  • Nonlinear equations
  • Two-step methods
  • Efficiency index
  • Order of convergence
  • Simple root
  • Iterative method with memory
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Computational Mathematics and Computer Modeling with Applications (CMCMA)
Volume 1, Issue 2 - Serial Number 2
December 2022
Pages 20-26
Files
  • XML
  • PDF 83.3 K
History
  • Receive Date: 19 August 2022
  • Revise Date: 16 September 2022
  • Accept Date: 21 September 2022
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How to cite
  • RIS
  • EndNote
  • Mendeley
  • BibTeX
  • APA
  • MLA
  • HARVARD
  • CHICAGO
  • VANCOUVER
Statistics
  • Article View: 180
  • PDF Download: 289

APA

Erfanifar, R. (2022). A class of efficient derivative free iterative method with and without memory for solving nonlinear equations. Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(2), 20-26. doi: 10.52547/CMCMA.1.2.20

MLA

Erfanifar, R. . "A class of efficient derivative free iterative method with and without memory for solving nonlinear equations", Computational Mathematics and Computer Modeling with Applications (CMCMA), 1, 2, 2022, 20-26. doi: 10.52547/CMCMA.1.2.20

HARVARD

Erfanifar, R. (2022). 'A class of efficient derivative free iterative method with and without memory for solving nonlinear equations', Computational Mathematics and Computer Modeling with Applications (CMCMA), 1(2), pp. 20-26. doi: 10.52547/CMCMA.1.2.20

CHICAGO

R. Erfanifar, "A class of efficient derivative free iterative method with and without memory for solving nonlinear equations," Computational Mathematics and Computer Modeling with Applications (CMCMA), 1 2 (2022): 20-26, doi: 10.52547/CMCMA.1.2.20

VANCOUVER

Erfanifar, R. A class of efficient derivative free iterative method with and without memory for solving nonlinear equations. Computational Mathematics and Computer Modeling with Applications (CMCMA), 2022; 1(2): 20-26. doi: 10.52547/CMCMA.1.2.20

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