Publications

Year of Publication: 2017
Authors: M. Hanke; R. März; C. Tischendorf; E. Weinmüller; S. Wurm
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 linear 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 linear higher-index differential–algebraic equations.

DOI: 10.1016/j.cam.2016.12.017
Corporate Authors: M. Hanke; R. März; C. Tischendorf; E. Weinmüller; S. Wurm
Date Published: 06/2017
Volume: 317
Publication Language: eng
Start Page: 403
Type of Publication: Journal Article
URL: http://www.sciencedirect.com/science/article/pii/S0377042716306276