structure a family of three-step with-memory methods for solving nonlinear equations and their dynamics1

In this paper, nonlinear equations are solved using thewith memory methods. then, by introducing the selfacceleratingparameter, a 27% 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.