Preprint 2016-07
Michael Hanke, Roswitha März, Caren Tischendorf, Ewa Weinmüller, Stefan Wurm
Least-Squares Collocation for Higher Index Differential-Algebraic Equations
Abstract: Differential-algebraic equations with higher index give rise to essentially ill-posed problems. Therefore, their numerical approximation requires special care. In the present paper, we state the notion of ill-posedness for differential-algebraic equations more precisely. Based on this property, we construct a regularization procedure using a least-squares collocation approach by discretizing the pre-image space. Numerical experiments show that the resulting method has excellent convergence properties and is not much more computationally expensive than standard collocation methods used in the numerical solution of ordinary differential equations or index-1 differential-algebraic equations. Convergence is shown for a limited class of higher index differential-algebraic equations.
Keywords: differential-algebraic equation, higher index, essentially ill-posed
problem, collocation, boundary value problem
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2016-07
36 pp.