Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Michael Hanke, Roswitha März and Caren Tischendorf

Least-Squares Collocation for Higher-Index Linear Differential-Algebraic Equations: Estimating the Instability Threshold

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.

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2017-06

31 pp.