Sixteenth-Order Steffensen-Ostrowski Approach for Nonlinear Problems with Applications in Celestial, Predator-Prey and Neural Activation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Sixteenth-Order Steffensen-Ostrowski Approach for Nonlinear Problems with Applications in Celestial, Predator-Prey and Neural Activation

Popis výsledku v původním jazyce

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&apos;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&apos;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.

Název v anglickém jazyce

Sixteenth-Order Steffensen-Ostrowski Approach for Nonlinear Problems with Applications in Celestial, Predator-Prey and Neural Activation

Popis výsledku anglicky

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&apos;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&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

European Journal of Pure and Applied Mathematics

ISSN

1307-5543

e-ISSN

—

Svazek periodika

18

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

26

Strana od-do

nestránkováno

Kód UT WoS článku

001487032000012

EID výsledku v databázi Scopus

2-s2.0-105004427663