论文标题
朝着可靠的最小二乘搭配实现高索引差异代数方程式
Towards a reliable implementation of least-squares collocation for higher-index differential-algebraic equations
论文作者
论文摘要
在本说明中，我们讨论了有关实施过度确定的最小二乘搭配方法的几个问题，以实现高分数差异代数方程（DAE）。由于较高的索引DAE在自然环境中导致了不足的问题，因此预计Dicrete对应物非常敏感，这对其实施特别重要。我们提供了强大的基础功能和搭配点来设计离散问题并证实其数值解决方案的过程。此外，证明了许多新的错误估计值，以支持某些设计决策。
In this note we discuss several questions concerning the implementation of overdetermined least-squares collocation methods for higher-index differential algebraic equations (DAEs). Since higher-index DAEs lead to ill-posed problems in natural settings, the dicrete counterparts are expected to be very sensitive, what attaches particular importance to their implementation. We provide a robust selection of basis functions and collocation points to design the discrete problem and substantiate a procedure for its numerical solution. Additionally, a number of new error estimates are proven that support some of the design decisions.
