Asymptotic expansions for regularization methods of linear fully implicit differential-algebraic equations (Q1332678)

One approach to studying higher index differential algebraic equations (DAEs) is to approximate then by DAEs of lower index. That is, by using regularization algorithms. This paper considers linear time varying DAEs, \(A(t)x'(t)+ B(t)x(t) = f(t)\), which are index two and three and satisfy certain additional technical assumptions. A regularization introduced by März for index two DAEs is generalized to the index three case. The structure of the regularized solutions and their convergence properties are characterized in terms of asymptotic expansions. This approach also characterizes what is known as the pencil regularization in the index two case.