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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Published in | Journal of mathematical chemistry Vol. 60; no. 8; pp. 1521 - 1541 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.09.2022
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0259-9791 1572-8897 |
DOI: | 10.1007/s10910-022-01371-6 |