A biparametric extension of King’s fourth-order methods and their dynamics
Autor:
Geum, Young Hee
; Kim, Young Ik
; Magreñán, Á. Alberto
Fecha:
05/2016Palabra clave:
Revista / editorial:
Applied Mathematics and ComputationCitación:
Young Hee Geum, Young Ik Kim, Á. Alberto Magreñán, A biparametric extension of King’s fourth-order methods and their dynamics, Applied Mathematics and Computation, Volume 282, 5 May 2016, Pages 254-275Tipo de Ítem:
Articulo Revista IndexadaResumen:
A class of two-point quartic-order simple-zero finders and their dynamics are investigated in this paper by extending King’s fourth-order family of methods. With the introduction of an error corrector having a weight function dependent on a function-to-function ratio, higher-order convergence is obtained. Through a variety of test equations, numerical experiments strongly support the theory developed in this paper. In addition, relevant dynamics of the proposed methods is successfully explored for a prototype quadratic polynomial as well as parameter spaces and dynamical planes.
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