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M. Hanke, R. März, C. Tischendorf, E. Weinmüller, S. Wurm:
"Least-Squares Collocation for Higher-Index Differential-Algebraic Equations";
Journal of Computational and Applied Mathematics, 317 (2017), 403 - 431.

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 di
ff
erential equations or index-1 di
ff
erential-
algebraic equations. Convergence is shown for a limited class of linear higher-index
di
ff
erential-algebraic equations.

di ff erential-algebraic equation, higher index, essentially ill-posed problem, collocation, boundary value problem, initial value problem

http://dx.doi.org/10.1016/j.cam.2016.12.017