The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative methods have been proposed in the literature. The evolution of these methods in terms of order of convergence implies the inclusion of a weight function for each case, showing an optimal fourth-order convergence, in the sense of Kung–Traub’s conjecture. The analysis of these new schemes is performed by means of complex dynamics. These methods are applied on the solution of the nonlinear Colebrook–White equation and the nonlinear system of the equilibrium conversion, both frequently used in Chemistry.

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CMMSE-2019 求解非线性化学问题的基于均值的迭代方法

Weerakoon 和 Fernando 设计的三阶迭代方法在其表达式中包含了两个函数评估的算术平均值。用不同的平均值代替这个算术平均值，文献中已经提出了其他迭代方法。这些方法在收敛阶数方面的演变意味着在每种情况下都包含一个权重函数，在 Kung-Traub 猜想的意义上显示出最佳的四阶收敛性。这些新方案的分析是通过复杂的动力学进行的。这些方法应用于非线性 Colebrook-White 方程和平衡转换的非线性系统的求解，这两种方法在化学中都经常使用。