Asymptotic Expansions for Regularization Methods of Linear Fully Implicit Differential-Algebraic Equations

Abstract

Differential-algebraic equations with a higher index can be approximated by regularization algorithms. One of such possibilities was introduced by März for linear time varying index 2 systems. In the present paper her approach is generalized to linear time varying index 3 systems. The structure of the regularized solutions and their convergence properties are characterized in terms of asymptotic expansions. In this way it is also possible to characterize the so-called pencil regularization in the index 2 case.