A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations

Abstract

We introduce a new class of optimal iterative methods without memory for approximating a simple root of a given nonlinear equation. The proposed class uses four function evaluations and one first derivative evaluation per iteration and it is therefore optimal in the sense of Kung and Traub's conjecture. We present the construction, convergence analysis and numerical implementations, as well as comparisons of accuracy and basins of attraction between our method and existing optimal methods for several test problems.

Optimal derivative-free root finding methods based on the Hermite interpolation

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Bifurcation and Chaos in Real Dynamics of a Two-Parameter Family Arising from Generating Function of Generalized Apostol-Type Polynomials

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Chaos in dynamics of a family of transcendental meromorphic functions

“…Since the Julia sets (chaotic sets) occur as one of the crucial component in these investigations, their various characterizations and identification of their intrinsic properties are primarily developed in these studies. This work has also applications in a number of diverse science and engineering areas wherein simulations of objects of fractal nature are needed [9,10,15,17,19,20,22,23]. Let C andĈ denote the complex plane and the extended complex plane respectively.…”