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


Creative Commons License

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

ADVANCES IN DIFFERENCE EQUATIONS, vol.2021, no.1, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-021-03616-1
  • Title of Journal : ADVANCES IN DIFFERENCE EQUATIONS
  • 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.