Optimal Fourth- and Eighth-order iterative solver and their basins of attraction
Keywords:
Basins of attraction, Multi-point iterations, Non-linear equationAbstract
We developed a new, fourth- and eighth-order optimal approach for solving nonlinear
equations in this study. With three function evaluations, the new methods’ convergence
order is four; with four function evaluations, it is eight. Furthermore, according to the
Kung-Traub hypothesis, it is optimal. In comparison to the suggested approaches, numerical
results are provided to verify the superior computing efficiency of the current robust
methods. We examine a wide range of practical issues, including projectile velocity to verify
the suitability and efficacy of our suggested approaches. Lastly, in order to illustrate their
dynamic behaviour on the complex plane, the basins of attraction are also provided.
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