2 research outputs found
An optimal family of eighth-order simple root finders with weight functions dependent on function-to-function ratios and their dynamics underlying extraneous fixed points
The article of record as published may be found at http://dx.doi.org/10.1016/j.cam.2016.11.036We extend in this paper an optimal family of three-step eighth-order methods developed
by Džunić et al. (2011) with higher-order weight functions employed in the second and third
sub-steps and investigate their dynamics under the relevant extraneous fixed points among which
purely imaginary ones are specially treated for the analysis of the rich dynamics. Their
theoretical and computational properties are fully investigated along with a main theorem
describing the order of convergence and the asymptotic error constant as well as proper choices of
special cases. A wide variety of relevant numerical examples are illustrated to confirm the
underlying theoretical development. In addition, this paper investigates the dynamics of selected
existing optimal eighth-order iterative maps with the help of illustrative basins of attraction for
various polynomials.Research Fund of Dankook Universit