Next Article in Journal
Nonlinear Spatiotemporal Viral Infection Model with CTL Immunity: Mathematical Analysis
Previous Article in Journal
Fractional Derivatives for Economic Growth Modelling of the Group of Twenty: Application to Prediction
Previous Article in Special Issue
Extending the Applicability of Stirling’s Method
Open AccessArticle

Bifurcations along the Boundary Curves of Red Fixed Components in the Parameter Space for Uniparametric, Jarratt-Type Simple-Root Finders

Department of Applied Mathematics, Dankook University, Cheonan 330-714, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 51; https://doi.org/10.3390/math8010051
Received: 23 November 2019 / Revised: 18 December 2019 / Accepted: 25 December 2019 / Published: 1 January 2020
(This article belongs to the Special Issue Multipoint Methods for the Solution of Nonlinear Equations)
Bifurcations have been studied with an extensive analysis of boundary curves of red, fixed components in the parametric space for a uniparametric family of simple-root finders under the Möbius conjugacy map applied to a quadratic polynomial. An elementary approach from the perspective of a plane curve theory properly describes the geometric figures resembling a circle or cardioid to characterize the underlying boundary curves that are parametrically expressed. Moreover, exact bifurcation points for satellite components on the boundaries have been found, according to the fact that the tangent line at a bifurcation point simultaneously touches the red fixed component and the satellite component. Computational experiments implemented with examples well reflect the significance of the theoretical backgrounds pursued in this paper. View Full-Text
Keywords: parameter space; Möbius map; bifurcation point; Jarratt’s method; cardioid-like; circle-like parameter space; Möbius map; bifurcation point; Jarratt’s method; cardioid-like; circle-like
Show Figures

Figure 1

MDPI and ACS Style

Lee, M.-Y.; Kim, Y.I. Bifurcations along the Boundary Curves of Red Fixed Components in the Parameter Space for Uniparametric, Jarratt-Type Simple-Root Finders. Mathematics 2020, 8, 51.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop