Structure A Family Of Three-Step With-Memory Methods For Solving Nonlinear Equations And Their Dynamics1

In this paper, nonlinear equations are solved using the with memory methods. Then, by introducing the selfaccelerating parameter, a 27% percent improvement in the convergence order have been obtained. The proposed method does not need to calculate the function derivative. Finally, numerical comparisons have been accomplished to show the proficiency of the proposed method. Also, the absorption and stability area of the proposed method has been given for different values of the self-accelerator parameter.