A biparametric extension of King’s fourth-order methods and their dynamics

Young Hee Geum, Young Ik Kim and Á. Alberto Magreñán

Applied Mathematics and Computation, 2016, vol. 282, issue C, 254-275

Abstract: 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.

Keywords: Parameter space; Error corrector; Dynamical plane; King’s fourth-order method (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:282:y:2016:i:c:p:254-275

DOI: 10.1016/j.amc.2016.02.020

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