Sixteenth-Order Steffensen-Ostrowski Approach for Nonlinear Problems with Applications in Celestial, Predator-Prey and Neural Activation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10258151" target="_blank" >RIV/61989100:27740/25:10258151 - isvavai.cz</a>
Result on the web
<a href="https://www.ejpam.com/index.php/ejpam/article/view/5822" target="_blank" >https://www.ejpam.com/index.php/ejpam/article/view/5822</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.29020/nybg.ejpam.v18i2.5822" target="_blank" >10.29020/nybg.ejpam.v18i2.5822</a>
Alternative languages
Result language
angličtina
Original language name
Sixteenth-Order Steffensen-Ostrowski Approach for Nonlinear Problems with Applications in Celestial, Predator-Prey and Neural Activation
Original language description
The increasing demand for accurate and efficient solutions to nonlinear equations, driven by advancements across diverse research and engineering fields, highlights the critical need for innovative computational methods. This study addresses this need by introducing a novel derivative-free sixteenth-order iterative scheme derived from a weighted Steffensen-Ostrowski-type family. According to the Kung-Traub conjecture, this scheme is designed to achieve optimal convergence using only five function evaluations per iteration. A key innovation lies in employing a bivariate weight function in the third step and Lagrange interpolation in the fourth step, ensuring high accuracy and computational efficiency by avoiding derivative evaluation. The extensive convergence analysis shows that the proposed scheme is of sixteenth order and is validated through applications to real-world problems, including Kepler's celestial motion, an ideally mixed reactor, predator-prey models, neural activation dynamics, and periodic ecosystem growth. Numerical results demonstrate the superiority of the proposed scheme over existing four-point iterative schemes, particularly in terms of absolute error and computational convergence order. Furthermore, graphical analysis of complex polynomials illustrates the algorithm's attraction basins, offering a wide range of choosing from initial guesses to converge to the specified root more efficiently without divergence and hence showed more stable behavior. In this way we achieved significant computational improvements and higher convergence order. As the proposed scheme fall under the category of derivative free schemes, so it is more general as compared to existing schemes in literature and is considered to be a good alternative to the existing schemes especially where derivatives are unavailable.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics
Result continuities
Project
—
Continuities
O - Projekt operacniho programu
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
European Journal of Pure and Applied Mathematics
ISSN
1307-5543
e-ISSN
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Volume of the periodical
18
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
nestránkováno
UT code for WoS article
001487032000012
EID of the result in the Scopus database
2-s2.0-105004427663