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Multipoint Iterative Methods for Finding All the Simple Zeros in an Interval

Author

Listed:
  • T. Lotfi
  • F. Soleymani
  • S. Sharifi
  • S. Shateyi
  • F. Khaksar Haghani

Abstract

Two new families of multipoint without memory iterative methods with eighth‐ and sixteenth‐orders are constructed using the symbolic software Mathematica. The key idea in constructing such methods is based on producing some generic suitable functions to reduce the functional evaluations and increase the order of convergence along the computational efficiency. Again by applying Mathematica, we design a hybrid algorithm to capture all the simple real solutions of nonlinear equations in an interval. The application of the new schemes in producing fractal pictures is also furnished.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:601205
    DOI: 10.1155/2014/601205
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    References listed on IDEAS

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    1. F. Soleymani & M. Sharifi & S. Shateyi, 2014. "Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, March.
    2. F. Soleymani & M. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "A Class of Steffensen-Type Iterative Methods for Nonlinear Systems," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, April.
    3. F. Soleymani & M. Sharifi & S. Shateyi, 2014. "Approximating the Inverse of a Square Matrix with Application in Computation of the Moore‐Penrose Inverse," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    4. 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).
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    Cited by:

    1. Mohammed Barrada & Mariya Ouaissa & Yassine Rhazali & Mariyam Ouaissa, 2020. "A New Class of Halley’s Method with Third‐Order Convergence for Solving Nonlinear Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    2. Krzysztof Gdawiec & Wiesław Kotarski & Agnieszka Lisowska, 2015. "Polynomiography Based on the Nonstandard Newton‐Like Root Finding Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).
    3. T. Lotfi & F. Soleymani & S. Shateyi & P. Assari & F. Khaksar Haghani, 2014. "New Mono‐ and Biaccelerator Iterative Methods with Memory for Nonlinear Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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