In this paper, we develop some variants of the well-known Halley’s iterative method to solve nonlinear equations. The resulting methods are one-step methods, with and without memory, which use different number of functional evaluations per iteration. Those with memory have higher efficiency indexes than Newton’s scheme and also than many known optimal iterative procedures without memory. Their dependence on the initial estimation is studied by using real multidimensional dynamical techniques, showing their stable behavior. This is also checked with some numerical examples, that illustrate the performance of the proposed methods compared with other well-known schemes in the literature. For all the examples considered, that include chemical equilibrium problems, global reaction rates in packed bed reactors or continuous stirred tank reactors, the methods with memory reach the approximations to the roots, within the established tolerance, using fewer number of functional evaluations than their partners.

中文翻译：

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具有记忆的哈雷方法的一些变体及其在解决几个化学问题中的应用

在本文中，我们开发了著名的哈雷迭代法的一些变体来求解非线性方程。由此产生的方法是一步法，有记忆和没有记忆，每次迭代使用不同数量的功能评估。那些有记忆的具有比牛顿方案更高的效率指标，也比许多已知的没有记忆的最优迭代过程更高。通过使用真实的多维动力学技术研究了它们对初始估计的依赖性，显示了它们的稳定行为。这也通过一些数值例子进行了检查，这些例子说明了与文献中其他众所周知的方案相比所提出的方法的性能。对于所有考虑的例子，包括化学平衡问题、填充床反应器或连续搅拌釜反应器中的全局反应速率，