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

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

Mathematical Problems in Engineering, 2018, vol. 2018, 1-12

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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:8093673

DOI: 10.1155/2018/8093673

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