Creating a new two-step recursive memory method with eight-order based on Kung and Traub's method.

• Torkashvand, Vali ^[1] ; Momenzadeh, Mohammad ^[1] ; Lotf, Taher ^[2]
  1. [1] Islamic Azad University

     Islamic Azad University

     Irán

     
  2. [2] 3Islamic Azad University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 5, 2020, págs. 1167-1189
• Idioma: inglés
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• Resumen

  • We are devoted to the study of an iterative recursive Traub-Steffensen like method for approximating the simple roots of a nonlinear equation. Using the recursive technique, the R-order of convergence is increased from 4 to 8 without any new function evaluations, which means 100% improvement of the order of the convergence. The theoretical study of the convergence rate is investigated and demonstrated. A few nonlinear problems are presented to justify the theoretical study.