Year: 2025
Type: article
Abstract: Some optimal and non-optimal iterative approaches for computing multiple zeros of nonlinear functions have recently been published in the literature when the multiplicity θ 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.
Source: Mathematics
DOI: 10.3390/math13030523
Authors: Sunil Kumar, Monika Khatri, Muktak Vyas, Ashwini Kumar, Priti Dhankhar, Lorentz Jäntschi
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4407186156