Abstract There have appeared in the literature a lot of optimal eighth-order iterative methods for approximating simple zeros of nonlinear functions. Although, the similar ideas can be extended for the case of multiple zeros but the main drawback is that the order of convergence and computational efficiency reduce dramatically. Therefore, in order to retain the accuracy and convergence order, several optimal and non-optimal modifications have been proposed in the literature. But, as far as we know, there are limited number of optimal eighth-order methods that can handle the case of multiple zeros. With this aim, a wide general class of optimal eighth-order methods for multiple zeros with known multiplicity is brought forward, which is based on weight function technique involving function-to-function ratio. An extensive convergence analysis is demonstrated to establish the eighth-order of the developed methods. The numerical experiments considered the superiority of the new methods for solving concrete variety of real life problems coming from different disciplines such as trajectory of an electron in the air gap between two parallel plates, the fractional conversion in a chemical reactor, continuous stirred tank reactor problem, Planck’s radiation law problem, which calculates the energy density within an isothermal blackbody and the problem arising from global carbon dioxide model in ocean chemistry, in comparison with methods of similar characteristics appeared in the literature.

中文翻译：

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一类稳定的类修正牛顿法，用于多根及其动力学

摘要 文献中出现了许多逼近非线性函数简单零点的最优八阶迭代方法。虽然，类似的想法可以扩展到多个零的情况，但主要缺点是收敛的阶数和计算效率急剧下降。因此，为了保持精度和收敛顺序，文献中提出了几种最优和非最优的修改。但是，据我们所知，可以处理多个零的情况的最优八阶方法数量有限。为此，提出了一类广泛的通用类的具有已知多重性的多个零点的最优八阶方法，该方法基于涉及函数与函数比的权函数技术。展示了广泛的收敛分析，以建立所开发方法的八阶。数值实验考虑了解决来自不同学科的具体各种现实生活问题的新方法的优越性，例如电子在两个平行板之间的气隙中的轨迹，化学反应器中的分数转化，连续搅拌釜反应器问题, 普朗克辐射定律问题，计算等温黑体内的能量密度，以及海洋化学中全球二氧化碳模型产生的问题，与文献中出现的类似特征的方法进行比较。