A Decomposition Method Of Nonstandard Linear Singular Perturbation System

The paper is mainly about the linear nonstandard singular perturbation system of how to decompose it into slow subsystem and fast subsystem.The related differential algebraic system is simplified through a coordinate transformation in chapter two.Then, we successfully decompose the system of index 2, and obtain a procedure which can be programming with no difficulty.After that, we tried to decompose the system of index 3 in the same way as the index 2. To take advantage of the index 2, it takes effort to reduce index 3 to index 2,and we acquire some conclusion as lemma 4.1 which can reduce the index k and index k+1 after generalization. And for index n, we can get the similar conclusion by mathematical induction.For index n, we get main result all in chapter 5 and chapter 6. In chapter 6 we give out a approximated estimation between two subsystem and singular perturbation system of index n.