Extended Comparison between Two Derivative-Free Methods of Order Six for Equations under the Same Conditions

Under the same conditions, we propose extended comparison between two derivative free schemes of order six for addressing equations. The existing convergence technique used standard Taylor series approach, which requires derivatives up to seven. In contrast previous researchers, our theorems only demand first derivative. addition, formulas determining region uniqueness solution, radii, and error estimations are suggested. As a consequence, broaden utility these productive schemes. Moreover, present attraction basins obtain roots complex polynomial confirmation findings on application problems brings this research close.