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__Convergence issues of DAEs with non-constant constraints__

L. Jansen

**Abstract**

Two of the best known DAE solver packages are DASSL and RADAU. While RADAU is based on the Radau IIA method, DASSL uses BDF-methods to solve a DAE.
The BDF-methods as well as the Radau IIA method may fail to provide a convergent numerical solution for linear DAEs with time depending constraints.
In particular these methods do not converge if applied to the following well known example:
$
x_1'+\eta t x_2' + (1+\eta)x_2 &= 0 ,
x_1 +\eta t x_2 &= e^{-t},
$
with $\eta < -0.5$, [1]. While other prominent methods like Lobatto IIIA share the same convergence problem we present a class of discontinuous collocation methods which overcomes this weakness.

**Bibliography**

[1]
R. Lamour, R. März and C. Tischendorf,
Differential Algebraic Equations: A Projector Based Analysis,
Springer, 2013.