用正则化方法求解代数-微分方程组(英文)

Regularization Methods for the Treatment of Differential-Algebraic Equations

由于代数－微分方程组可看作是无限刚性常微分方程组，因而代数－微分方程组的解可看作是刚性常微分方程组的解在某种意义下的极限．对于指标小于３的半显式Ｈｅｓｓｅｎｂｅｒｇ型，本文给出了正则化方法．数值例子显示了具体的正则化过程．

This paper deals with the regularization methods for the treatment of DAEs.One can interpret DAEs as infinitely stiff ODEs,so the solutions of DAEs can be considered as the limit of the solutions to the stiff ODEs in a certain sense.Semi explicit DAEs in Hessenberg form with index less than 3 can be regularized to a stiff ODEs by using the technique in this paper.A numerical example is given to show the detailed regularization process.