Krylov-ROW methods for DAEs of index 1 with applications to viscoelasticity

The combination of Krylov techniques to Rosenbrock methods (Krylov-ROW methods) leads to an efficient class of methods for stiff problems. Here the extension to semi-explicit DAEs of index 1 is discussed. Several paths are possible to apply the direct and the indirect approach. The equivalence of different approaches is proved. Conclusions on the dimension of the Krylov spaces are drawn. The methods are applied to typical high-dimensional DAEs arising from viscoelastic materials. Numerical experiments confirm the theoretical predictions.