Numerical scheme for estimating all roots of non-linear equations with applications

The roots of non-linear equations are a major challenge in many scientific and professional fields. This problem has been approached in a number of ways, including use of the sequential Newton's method and the traditional Weierstrass simultaneous iterative scheme. To approximate all of the root...

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Bibliographic Details
Published in:AIMS mathematics Vol. 8; no. 10; pp. 23603 - 23620
Main Authors: Shams, Mudassir, Kausar, Nasreen, Araci, Serkan, Oros, Georgia Irina
Format: Journal Article
Language:English
Published: AIMS Press 01.01.2023
Subjects:
computational efficiency
computer algorithm
error graph
simultaneous methods
ISSN:2473-6988, 2473-6988
Online Access:Get full text
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Summary:The roots of non-linear equations are a major challenge in many scientific and professional fields. This problem has been approached in a number of ways, including use of the sequential Newton's method and the traditional Weierstrass simultaneous iterative scheme. To approximate all of the roots of a given nonlinear equation, sequential iterative algorithms must use a deflation strategy because rounding errors can produce inaccurate results. This study aims to develop an efficient numerical simultaneous scheme for approximating all nonlinear equations' roots of convergence order 12. The numerical outcomes of the considered engineering problems show that, in terms of accuracy, validations, error, computational CPU time, and residual error, recently developed simultaneous methods perform better than existing methods in the literature.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20231200