In this paper, the local convergence analysis of the family of Kung-Traub’s two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by solving test problems from different chemical engineering application areas, e.g. Planck’s radiation law problem, natch distillation at infinite reflux, van der Waal’s equation, air gap between two parallel plates and flow in a smooth pipe, in order to check the applicability and effectiveness of our proposed methods.

中文翻译：

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关于 Kung-Traub 两点法的局部收敛性及其动力学

在本文中，获得了Kung-Traub 两点法族的局部收敛分析和该族的收敛球，并研究了所得族在二次和三次多项式上的动力学行为。我们使用复杂的动态工具来分析它们的稳定性，并表明这个家族的稳定成员的区域是巨大的。本研究还提供了数值示例。通过求解不同化学工程应用领域的测试问题，将该方法与几种广泛使用的求解方法进行比较，例如普朗克辐射定律问题、无限回流下的自然蒸馏、范德瓦尔方程、两个平行板之间的气隙和光滑管道中的流动，以检查我们提出的方法的适用性和有效性。