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A Class of Steffensen‐Type Iterative Methods for Nonlinear Systems

Author

Listed:
  • F. Soleymani
  • M. Sharifi
  • S. Shateyi
  • F. Khaksar Haghani

Abstract

A class of iterative methods without restriction on the computation of Fréchet derivatives including multisteps for solving systems of nonlinear equations is presented. By considering a frozen Jacobian, we provide a class of m‐step methods with order of convergence m + 1. A new method named as Steffensen‐Schulz scheme is also contributed. Numerical tests and comparisons with the existing methods are included.

Suggested Citation

  • F. Soleymani & M. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "A Class of Steffensen‐Type Iterative Methods for Nonlinear Systems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:705375
    DOI: 10.1155/2014/705375
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    References listed on IDEAS

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    1. Michael Trott, 2006. "The Mathematica GuideBook for Numerics," Springer Books, Springer, number 978-0-387-28814-7, March.
    2. Alicia Cordero & Fazlollah Soleymani & Juan R. Torregrosa & Stanford Shateyi, 2014. "Basins of Attraction for Various Steffensen‐Type Methods," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Wei-Xiang Wang & You-Lin Shang & Wei-Gang Sun & Ying Zhang, 2011. "Finding the Roots of System of Nonlinear Equations by a Novel Filled Function Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    4. Alicia Cordero & Fazlollah Soleymani & Juan R. Torregrosa & Stanford Shateyi, 2014. "Basins of Attraction for Various Steffensen-Type Methods," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-17, March.
    5. Eman S. Alaidarous & Malik Zaka Ullah & Fayyaz Ahmad & A.S. Al-Fhaid, 2013. "An Efficient Higher‐Order Quasilinearization Method for Solving Nonlinear BVPs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    6. Eman S. Alaidarous & Malik Zaka Ullah & Fayyaz Ahmad & A.S. Al-Fhaid, 2013. "An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-11, November.
    7. Wei-Xiang Wang & You-Lin Shang & Wei-Gang Sun & Ying Zhang, 2011. "Finding the Roots of System of Nonlinear Equations by a Novel Filled Function Method," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-9, November.
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    Cited by:

    1. T. Lotfi & F. Soleymani & S. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "Multipoint Iterative Methods for Finding All the Simple Zeros in an Interval," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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