System of linear ordinary differential and differential-algebraic equations and pseudo-spectral method

In this paper, first we introduce, briefly, pseudo-spectral method to solve linear Ordinary Differential Equations (ODEs), and then extend it to solve a system of linear ODEs and then Differential-Algebraic Equations (DAEs). Furthermore, because of appropriate choice of Chebyshev Gauss Raudo points we will show that this method can be used to solve a DAE whenever some coefficient functions in constraint are not analytic by providing some numerical examples.