On highly efficient derivative-free family of numerical methods for solving polynomial equation simultaneously


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Shams M., Rafiq N., Kausar N., Agarwal P., Park C., Mir N. A.

ADVANCES IN DIFFERENCE EQUATIONS, vol.2021, no.1, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-021-03616-1
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Numerical scheme, Polynomials, Computational efficiency, CPU-time, Convergence order, ROOT-FINDING METHODS, ITERATIVE METHODS, SIMULTANEOUS APPROXIMATION, NONLINEAR EQUATIONS, CONVERGENCE, ZEROS, DISTINCT

Abstract

A highly efficient new three-step derivative-free family of numerical iterative schemes for estimating all roots of polynomial equations is presented. Convergence analysis proved that the proposed simultaneous iterative method possesses 12th-order convergence locally. Numerical examples and computational cost are given to demonstrate the capability of the method presented.