In this paper, we construct a derivative-free multi-step iterative scheme based on Steffensen’s method. To avoid excessively increasing the number of functional evaluations and, at the same time, to increase the order of convergence, we freeze the divided differences used from the second step and use a weight function on already evaluated operators. Therefore, we define a family of multi-step methods with convergence order $2m$, where $m$ is the number of steps, free of derivatives, with several parameters and with dynamic behaviour, in some cases, similar to Steffensen’s method. In addition, we study how to increase the convergence order of the defined family by introducing memory in two different ways: using the usual divided differences and the Kurchatov divided differences. We perform some numerical experiments to see the behaviour of the proposed family and suggest different weight functions to visualize with dynamical planes in some cases the dynamical behaviour.

在本文中，我们构建了一个基于Steffensen 方法的无导数多步迭代方案。为了避免过度增加功能评估的数量，同时增加收敛的顺序，我们冻结了第二步中使用的划分差异，并在已经评估的算子上使用权重函数。因此，我们定义了一系列具有收敛顺序的多步方法$\mathrm{2个}米$， 在哪里$米$是步数，没有导数，有几个参数和动态行为，在某些情况下，类似于 Steffensen 的方法。此外，我们研究了如何通过以两种不同的方式引入记忆来增加定义族的收敛阶数：使用通常的划分差异和Kurchatov划分差异。我们进行了一些数值实验以查看所提出的家族的行为，并建议使用不同的权重函数在某些情况下使用动态平面可视化动态行为。