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, cilt.2021, sa.1, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2021 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1186/s13662-021-03616-1
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Numerical scheme, Polynomials, Computational efficiency, CPU-time, Convergence order, ROOT-FINDING METHODS, ITERATIVE METHODS, SIMULTANEOUS APPROXIMATION, NONLINEAR EQUATIONS, CONVERGENCE, ZEROS, DISTINCT
  • Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

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.