Efficient family of three-step with-memory methods and their dynamics..

Torkashvand, Vali; Kazemi, Manochehr; Azimi, Masoud

doi:10.22034/cmde.2023.55761.2324

Efficient family of three-step with-memory methods and their dynamics..

Document Type : Research Paper

Authors

¹ Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Shahr-e-Qods, Iran.

² Department of Mathematics , Farhangian University , Tehran, Iran.

³ Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran.

10.22034/cmde.2023.55761.2324

Abstract

In this work, we have proposed a general manner to extend some twoparametric
with-memory methods to obtain simple roots of nonlinear equations.
Novel improved methods are two-step without memory and have two
self-accelerator parameters that do not have additional evaluation. The methods
have been compared with the nearest competitions in various numerical
examples. Anyway, the theoretical order of convergence is verified. The basins
of attraction of the suggested methods are presented and corresponded to explain
their interpretation.

Keywords