Vali Torkashvand - Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Shahr-e-Qods, Iran.
Manochehr Kazemi - Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran.
Masoud Azimi - Department of Mathematics , Farhangian University , Tehran, Iran.

In this work, we have proposed a general manner to extend some two-parametric 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.

With-memory method, Basin of attraction, Accelerator parameter, R-order convergence, Nonlinear equations