论文标题
固有ODE的离散化和DAE与对称的几何整合
Discretization of inherent ODEs and the geometric integration of DAEs with symmetries
论文作者
论文摘要
考虑到基于相关固有的普通微分方程（ODE）的集成，考虑了微分 - 代数方程（DAE）的离散方法。这允许使用任何适合ODE的数值集成的离散化方案。对于具有对称性的DAE，可以表明固有的ODE可以构造，以使其继承给定DAE的对称属性和其流量的几何特性。这特别允许使用具有具有类似几何特性的数值流量的几何积分方案。
Discretization methods for differential-algebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE). This allows to make use of any discretization scheme suitable for the numerical integration of ODEs. For DAEs with symmetries it is shown that the inherent ODE can be constructed in such a way that it inherits the symmetry properties of the given DAE and geometric properties of its flow. This in particular allows the use of geometric integration schemes with a numerical flow that has analogous geometric properties.
