The recently developed new algorithm for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization opens new possibilities to apply Taylor series integration methods. In this paper, we show how corresponding projected explicit and implicit Taylor series methods can be adapted to DAEs of arbitrary index. Owing to our formulation as a projected optimization problem constrained by the derivative array, no explicit description of the inherent dynamics is necessary, and various Taylor integration schemes can be defined in a general framework. In particular, we address higher-order Padé methods that stand out due to their stability. We further discuss several aspects of our prototype implemented in Python using Automatic Differentiation. The methods have been successfully tested on examples arising from multibody systems simulation and a higher-index DAE benchmark arising from servo-constraint problems.

最近开发的新算法，用于使用基于投影仪的约束优化来为DAE计算一致的初始值和泰勒系数，为应用泰勒级数积分方法提供了新的可能性。在本文中，我们展示了如何将相应的投影显式和隐式泰勒级数方法适用于任意索引的DAE。由于我们将公式表示为受导数数组约束的计划优化问题，因此无需对固有动力学进行明确描述，并且可以在通用框架中定义各种泰勒积分方案。特别是，我们解决了因其稳定性而引人注目的高阶Padé方法。我们进一步讨论了使用自动差分在Python中实现的原型的几个方面。