Generalization of Liu–Zhou Method for Multiple Roots of Applied Science Problems

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Detalles Bibliográficos
Publicado en:	Mathematics vol. 13, no. 3 (2025), p. 523
Autor principal:	Kumar, Sunil
Otros Autores:	Khatri, Monika, Vyas, Muktak, Kumar, Ashwini, Dhankhar, Priti, Lorentz Jäntschi
Publicado:	MDPI AG
Materias:	Continuously stirred tank reactors Eigenvalues Iterative algorithms Methods Supersonic flow Iterative methods Hypotheses Neighborhoods Nonlinear equations
Acceso en línea:	Citation/Abstract Full Text + Graphics Full Text - PDF
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Descripción
Resumen:	Some optimal and non-optimal iterative approaches for computing multiple zeros of nonlinear functions have recently been published in the literature when the multiplicity <inline-formula>θ</inline-formula> of the root is known. Here, we present a new family of iterative algorithms for multiple zeros that are distinct from the existing approaches. Some special cases of the new family are presented and it is found that existing Liu-Zhou methods are the special cases of the new family. To check the consistency and stability of the new methods, we consider the continuous stirred tank reactor problem, isentropic supersonic flow problem, eigenvalue problem, complex root problem, and standard test problem in the numerical section and we find that the new methods are more competitive with other existing fourth-order methods. In the numerical section, the error of the new methods confirms their robust character.
ISSN:	2227-7390
DOI:	10.3390/math13030523
Fuente:	Engineering Database