Two new bi-accelerator iterative with memory methods for solving nonlinear equations

In this work, we introduce two new iterative methods with memory for approximating asimple zero of a nonlinear equation. These methods utilize two accelerators in eachiteration and improve their convergence order 75% without any new evaluation offunctions. Therefore, they are called with memory. To show the applicability andeffectiveness of the proposed methods, some numerical problems are examined.

Keywords:

Nonlinear equation , With memory method , R-order of convergence , Self accelerating parameter , Efficiency index