Journal of Computational and Applied Mathematics
Rosenbrook methods for differential algebraic equations
Numerische Mathematik
Using Krylov methods in the solution of large-scale differential-algebraic systems
SIAM Journal on Scientific Computing
Matrix-free W-methods using a multiple Arnoldi iteration
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
A class of linearly-implicit Runge-Kutta methods for multibody systems
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
ROWMAP—a ROW-code with Krylov techniques for large stiff ODEs
Applied Numerical Mathematics - Special issue on time integration
Exponential Integrators for Large Systems of Differential Equations
SIAM Journal on Scientific Computing
Runge---Kutta methods in elastoplasticity
Applied Numerical Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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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.