Time integration of index 1 DAEs with Rosenbrock methods using Krylovsubspace techniques

Abstract

The derivation of Rosenbrock‐Krylov methods for index 1 DAEs involves two well known techniques: a limit process which transforms a singular perturbed ODE to an index 1 DAE and the use of Krylov iterations instead of direct linear solvers for the stage equations. We show that our derived class of Rosenbrock‐Krylov schemes is independent of the order in which we apply these techniques. We also conclude that for convergence a rather accurate solution of the algebraic part is always needed.