Sequential Regularization Methods for higher index DAEs with constraint singularities: I. Linear Index-2 Case

Standard stabilization techniques for higher index DAEs often involve elimination of the algebraic solution components. This may not work well if there are singularity points where the constraints Jacobian matrix becomes rank-deficient. This paper proposes instead a sequential regularization method (SRM) -- a functional iteration procedure for solving problems with isolated singularities which have smooth differential solution components. For linear index-2 DAEs we consider both initial and boundary value problems. The convergence of the SRM is described and proved in detail. Various aspects of the subsequent numerical discretization of the regularized problems are discussed as well and some numerical verifications are carried out.