Pseudospectral method for numerical solution of DAEs with an error estimation

In [E. Babolian, M.M. Hosseini, Reducing index, and pseudospectral methods for differential-algebraic equations, Appl. Math. Comput. 140 (2003) 77-90], numerical solution of linear differential-algebraic equations (DAEs) has been presented by pseudospectral method. In this paper, a new error estimation technique is proposed to pseudospectral method such that is well done for linear semi-explicit DAEs. When the DAEs has index 2, the obtained approximate solution can be improved by using the proposed error estimation technique. Furthermore, with providing some examples the proposed error estimation method is dealt with numerically.