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

Mudassir Shams; Nasreen Kausar; Serkan Araci; Georgia Irina Oros; Mudassir Shams; Nasreen Kausar; Serkan Araci; Georgia Irina Oros

doi:10.3934/math.20231200

AIMS Mathematics

2023, Volume 8, Issue 10: 23603-23620. doi: 10.3934/math.20231200

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

1.
Department of Mathematics and Statistics, Riphah International University I-14, Islamabad 44000, Pakistan
2.
Department of Mathematics, Yildiz Technical University, Faculty of Arts and Science, Esenler, 34220, Istanbul, Türkiye
3.
Department of Basic Sciences, Faculty of Engineering, Hasan Kalyoncu University, Gaziantep TR-27010, Türkiye
4.
Department of Mathematics and Computer Science, University of Oradea, Oradea 410087, Romania

Received: 04 June 2023 Revised: 17 July 2023 Accepted: 17 July 2023 Published: 31 July 2023
MSC : 65H04, 65H05, 65Y05, 65M12

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.
- simultaneous methods,
- error graph,
- computational efficiency,
- computer algorithm
Citation: Mudassir Shams, Nasreen Kausar, Serkan Araci, Georgia Irina Oros. Numerical scheme for estimating all roots of non-linear equations with applications[J]. AIMS Mathematics, 2023, 8(10): 23603-23620. doi: 10.3934/math.20231200

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Abstract

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.

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