@article{HankeMaerzTischendorf, author = {Hanke, Michael and M{\"a}rz, Roswitha and Tischendorf, Caren}, title = {Least-Squares Collocation for Higher-Index Linear Differential-Algebraic Equations: Estimating the Instability Threshold}, series = {Math. Comp.}, volume = {88}, journal = {Math. Comp.}, doi = {10.1090/mcom/3393}, pages = {1647 -- 1683}, abstract = {Differential-algebraic equations with higher index give rise to essentially ill-posed problems. The least-squares collocation by discretizing the pre-image space is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations and index-1 differential-algebraic equations. This approach has displayed excellent convergence properties in numerical experiments, however, theoretically, till now convergence could be established merely for regular linear differential-algebraic equations with constant coefficients. We present now an estimate of the instability threshold which serves as the basic key for proving convergence for general regular linear DAEs.}, language = {en} }