In this work, we propose a new approach to the problem of critical point calculation, based on the formulation of Heidemann and Khalil (1980). This leads to a $2 \times 2$ system of nonlinear algebraic equations in temperature and molar volume, which makes possible the prediction of critical points of the mixture through an adaptation of the technique of inversion of functions from the plane to the plane, proposed by Malta, Saldanha, and Tomei (1993). The results are compared to those obtained by three methodologies: ($i$) the classical method of Heidemann and Khalil (1980), which uses a double-loop structure, also in terms of temperature and molar volume; ($ii$) the algorithm of Dimitrakopoulos, Jia, and Li (2014), which employs a damped Newton algorithm and ($iii$) the methodology proposed by Nichita and Gomez (2010), based on a stochastic algorithm. The proposed methodology proves to be robust and accurate in the prediction of critical points, as well as provides a global view of the nonlinear problem.

中文翻译：

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通过函数的数值反演计算临界点

在这项工作中，我们基于 Heidemann 和 Khalil (1980) 的公式提出了一种解决临界点计算问题的新方法。这导致了一个 $2\times 2$ 的温度和摩尔体积非线性代数方程系统，这使得通过适应从平面到平面的函数反演技术来预测混合物的临界点成为可能，提出了马耳他、萨尔达尼亚和托梅 (1993)。将结果与通过三种方法获得的结果进行比较： ($i$) Heidemann 和 Khalil (1980) 的经典方法，它使用双环结构，也在温度和摩尔体积方面；($ii$) Dimitrakopoulos、Jia 和 Li (2014) 的算法，该算法采用阻尼牛顿算法和 ($iii$) Nichita 和 Gomez (2010) 提出的方法，基于随机算法。所提出的方法在关键点的预测中被证明是稳健和准确的，并且提供了非线性问题的全局视图。