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

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  • 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, Hindawi, vol. 2014, pages 1-13, July.
    • Handle: RePEc:hin:jnljam:601205
    DOI: 10.1155/2014/601205
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    Cited by:

    1. Lateef Olakunle Jolaoso & Safeer Hussain Khan & Kazeem Olalekan Aremu, 2022. "Dynamics of RK Iteration and Basic Family of Iterations for Polynomiography," Mathematics, MDPI, vol. 10(18), pages 1-16, September.

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