Structure A Family Of Three-Step With-MemoryMethods For Solving Nonlinear Equations AndTheir Dynamics۱

In this paper, nonlinear equations are solved using thewith memory methods. Then, by introducing the selfacceleratingparameter, a ۲۷% percent improvement in theconvergence order have been obtained. The proposed methoddoes not need to calculate the function derivative. Finally,numerical comparisons have been accomplished to show theproficiency of the proposed method. Also, the absorption andstability area of the proposed method has been given fordifferent values of the self-accelerator parameter.

Keywords:

Accelerator parameter , Nonlinear equations , R-order convergence , Simple roots , With-memory method