In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because we only need this condition to guarantee convergence. As a result, the applicability of the method is expanded. We also use different convergence planes to show family behavior. Finally, the new results are used to solve some applications related to chemistry.

中文翻译：

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国王样两步法的局部收敛性和动力学研究及其应用

在本文中，我们介绍了两步King-like方法收敛的局部结果，以近似求解非线性方程组。在本研究中，我们仅将条件应用于一阶导数，因为我们仅需要此条件即可保证收敛。结果，扩展了该方法的适用性。我们还使用不同的收敛平面来显示家庭行为。最后，新结果用于解决与化学有关的一些应用。