Parametric Family of Root-Finding Iterative Methods: Fractals of the Basins of Attraction

Research interest in iterative multipoint schemes to solve nonlinear problems has increased recently because of the drawbacks point-to-point methods, which need high-order derivatives increase order convergence. However, this is not only key element classify schemes. We aim design new fixed point classes without memory, that improve or bring together existing ones different areas such as computational efficiency, stability and also convergence order. In manuscript, we present a family parametric whose four, been designed by using composition weight function techniques. A qualitative analysis made, based on complex discrete dynamics, select those elements class with best properties low-degree polynomials. This stable behavior directly related simplicity fractals defined basins attraction. opposite, particular methods unstable performance high-complexity their basins. The members are demonstrated be terms numerical non-polynomial functions, special emphasis Colebrook-White equation, wide applications Engineering.