Alicia Cordero

TL;DR: The classical King's family of fourth-order schemes is obtained as an special case and the conjugacy classes and dynamics of some of the presented methods for complex polynomials of different degrees are described.

TL;DR: This paper proposes a sixth-order family of Jarratt type methods for solving nonlinear equations and extends this family to the multidimensional case preserving the order of convergence.

TL;DR: Several iterative methods for solving nonlinear equations whose common origin is the classical Chebyshev’s method, using fractional derivatives in their iterative expressions are proposed, resulting in a robust performance for values of α close to one and almost any initial estimation.

TL;DR: The Conformable fractional Newton-type method is introduced by using the so-called fractional derivative, proving its quadratic convergence, and the numerical results confirm the theory and improve the results obtained by classical Newton’s method.

TL;DR: A bi-parametric family of predictor-corrector iterative schemes with optimal fourth-order of convergence, for solving nonlinear equations, is presented and extended to the multidimensional case by using some algebraic manipulations and a divided difference operator.