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Efficient Four-Parametric with-and-without-Memory Iterative Methods Possessing High Efficiency Indices

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  • Alicia Cordero
  • Moin-ud-Din Junjua
  • Juan R. Torregrosa
  • Nusrat Yasmin
  • Fiza Zafar

Abstract

We construct a family of derivative-free optimal iterative methods without memory to approximate a simple zero of a nonlinear function. Error analysis demonstrates that the without-memory class has eighth-order convergence and is extendable to with-memory class. The extension of new family to the with-memory one is also presented which attains the convergence order and a very high efficiency index . Some particular schemes of the with-memory family are also described. Numerical examples and some dynamical aspects of the new schemes are given to support theoretical results.

Suggested Citation

  • Alicia Cordero & Moin-ud-Din Junjua & Juan R. Torregrosa & Nusrat Yasmin & Fiza Zafar, 2018. "Efficient Four-Parametric with-and-without-Memory Iterative Methods Possessing High Efficiency Indices," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-12, April.
    • Handle: RePEc:hin:jnlmpe:8093673
    DOI: 10.1155/2018/8093673
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