Rosenbrock-Krylov methods for large systems of differential equations (Q2878954)

The authors deal with Rosenbrock-Krylov-type methods for ordinary differential equations. The methods are developed for large systems which contain several time scales or serve as line system of partial differential equations. In contrast to the well-known Rosenbrock and Rosenbrock-W schemes, the introduced Rosenbrock-Krylov methods require to construct only one single Krylov-subspace per time step.NEWLINENEWLINE In addition, the authors present Rosenbrock-Krylov methods of order four with excellent stability properties, i.e., being either L-stable or stiffly accurate. When applied to the two-dimensional shallow water equations, the Rosenbrock-Krylov methods show superior to the Rosenbrock-W and Rosenbrock methods.