Construction of fourth-order optimal families of iterative methods and their dynamics

@article{Behl2015ConstructionOF,
  title={Construction of fourth-order optimal families of iterative methods and their dynamics},
  author={Ramandeep Behl and Alicia Cordero and Sandile Sydney Motsa and Juan R. Torregrosa},
  journal={Applied Mathematics and Computation},
  year={2015},
  volume={271},
  pages={89-101}
}
In this paper, we propose a general class of fourth-order optimal multi-point methods without memory for obtaining simple roots. This class requires only three functional evaluations (viz. two evaluations of function f(xn), f(yn) and one of its first-order derivative f (xn)) per iteration. Further, we show that the well-known Ostrowski’s method and King’s family of fourth-order procedures are special cases of our proposed schemes. One of the new particular subclasses is a biparametric family of… CONTINUE READING
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