An efficient class of optimal sixteenth-order root-finding methods and their basins of attraction

The principal aim of this research is to propose a new general sixteenth-order iterative scheme that is applicable to any existing multi-point fourth and eighth-order method based on Newton’s method as the first step. The advantages of the new iterative class are its high efficiency, a simple body s...

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Bibliographic Details
Published inJournal of mathematical chemistry Vol. 60; no. 8; pp. 1521 - 1541
Main Authors Ćebić, Dejan, Ralević, Nebojša M.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2022
Springer Nature B.V
Subjects
Chemical engineering
Chemistry
Chemistry and Materials Science
Iterative methods
Math. Applications in Chemistry
Original Paper
Physical Chemistry
Theoretical and Computational Chemistry
Nonlinear equation
Sixteenth-order methods
Optimal methods
Divided differences
Basins of attraction
65H05
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Summary:The principal aim of this research is to propose a new general sixteenth-order iterative scheme that is applicable to any existing multi-point fourth and eighth-order method based on Newton’s method as the first step. The advantages of the new iterative class are its high efficiency, a simple body structure and a simple general form of the error equation. In order to check the validity of the theoretical results, we employ several chemical engineering applications and academic test problems. The numerical results clearly confirm the theory and show the good numerical/dynamical performance of the new class compared to the recently developed methods of the same order.
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-022-01371-6