Next Article in Journal
A Lichnerowicz–Obata–Cheng Type Theorem on Finsler Manifolds
Next Article in Special Issue
A Third Order Newton-Like Method and Its Applications
Previous Article in Journal
Kempe-Locking Configurations
Previous Article in Special Issue
Hybrid Second Order Method for Orthogonal Projection onto Parametric Curve in n-Dimensional Euclidean Space
Open AccessArticle

An Efficient Family of Optimal Eighth-Order Multiple Root Finders

1
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
2
Instituto de Matemáticas Multidisciplinar, Universitat Politènica de València, 46022 València, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 310; https://doi.org/10.3390/math6120310
Received: 13 November 2018 / Revised: 3 December 2018 / Accepted: 5 December 2018 / Published: 7 December 2018
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)
Finding a repeated zero for a nonlinear equation f ( x ) = 0 , f : I R R has always been of much interest and attention due to its wide applications in many fields of science and engineering. Modified Newton’s method is usually applied to solve this kind of problems. Keeping in view that very few optimal higher-order convergent methods exist for multiple roots, we present a new family of optimal eighth-order convergent iterative methods for multiple roots with known multiplicity involving a multivariate weight function. The numerical performance of the proposed methods is analyzed extensively along with the basins of attractions. Real life models from life science, engineering, and physics are considered for the sake of comparison. The numerical experiments and dynamical analysis show that our proposed methods are efficient for determining multiple roots of nonlinear equations. View Full-Text
Keywords: nonlinear equations; multiple zeros; optimal iterative methods; higher order of convergence nonlinear equations; multiple zeros; optimal iterative methods; higher order of convergence
Show Figures

Figure 1

MDPI and ACS Style

Zafar, F.; Cordero, A.; Torregrosa, J.R. An Efficient Family of Optimal Eighth-Order Multiple Root Finders. Mathematics 2018, 6, 310.

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
Search more from Scilit
 
Search
Back to TopTop