An index reduction method for linear Hessenberg systems

In [E. Babolian, M.M. Hosseini, Reducing index, and pseudospectral methods for differential-algebraic equations, Appl. Math. Comput. 140 (2003) 77-90] a reducing index method has been proposed for some cases of semi-explicit DAEs (differential algebraic equations). In this paper, this method is generalized to more cases. Also, it is focused on Hessenberg index 2 systems and proposed reduction index method will be illustrated for this problem. The Hessenberg system and its obtained reduced index system are numerically solved through pseudospectral method. In addition, aforementioned methods will be considered by one example.