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

Shams M., KAUSAR N., Araci S., Oros G. I.

AIMS Mathematics, vol.8, no.10, pp.23603-23620, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 10
  • Publication Date: 2023
  • Doi Number: 10.3934/math.20231200
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.23603-23620
  • Keywords: computational efficiency, computer algorithm, error graph, simultaneous methods
  • Yıldız Technical University Affiliated: Yes


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.