On the convergence of spectral methods for the solution of linear descriptor systems

The problem of the convergence of spectral methods for the solution of linear time-invariant descriptor systems is discussed. To this aim the concept of distributional convergence is introduced since time responses of linear descriptor systems present impulsive behaviour. The use of the regularized operational matrix of integration makes it possible to find convergent approximations, in the distributional sense, of the impulsive components of the free response of linear time-invariant descriptor systems