微分代数方程系统的一类新的归约方法

New reduction method for the differential-algebraic system

针对高阶(k≥2 )微分代数方程系统的归约问题,给出并证明了它的一类新的归约方法。该方法通过构造相容映射簇,将高阶微分代数方程系统逐步归约成低阶微分方程系统,最终将其转换成系统构形空间上的常微分方程。同时给出其各阶寂点的充分条件。

Aimed at the problem of the differential-algebraic systems with higher index (k greater than or equal 2), a new explicit method of its reduction is given. By construction of admissible mapping families, this method can reduce the higher index DAEs to lower index DAEs effectively. Finally to ordinary differential equations based on its configuration space. In the mean time, some sufficient conditions of impasse points are presented. Lastly, two examples are given to make known its effects.