A computational approach to the investigation of bifurcations, based on the use of a special type of Hermite–Padé approximant, is presented. The first part of this study is a review of a singularity extraction technique based on the assumption that the given series is the local representation of an algebraic function in the independent variable. The principal merit of the procedure is its ability to reveal the underlying problem of the branches solution which are represented by the original series. In the final section, numerical results are presented for Dean flow and two problems coming from heat transfer modelling and whose solutions are obtained by means of a regular perturbation method.

中文翻译：

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Hermite–Padé近似在检测某些边值问题的奇异性中的应用

提出了一种计算分叉的计算方法，该方法基于特殊类型的Hermite-Padé近似值的使用。本研究的第一部分是对奇异性提取技术的回顾，该假设基于以下假设：给定级数是自变量中代数函数的局部表示。该程序的主要优点是能够揭示分支序列所代表的原始问题的潜在问题。在最后一节中，给出了关于Dean流动的数值结果以及传热建模带来的两个问题，并通过常规扰动方法获得了它们的解。