The shallow water equations in spherical geometry provide a prototype for developing and testing numerical algorithms for atmospheric circulation models. In a previous paper we have studied a spatial discretization of these equations based on an Osher-type finite-volume method on stereographic and latitude-longitude grids. The current paper is a companion devoted to time integration. Our main aim is to discuss and demonstrate a third-order, A-stable, Runge-Kutta-Rosenbrock method. To reduce the costs related to the linear algebra operations, this linearly implicit method is combined with approximate matrix factorization. Its efficiency is demonstrated by comparison with a classical third-order explicit Runge-Kutta method. For that purpose we use a known test set from literature. The comparison shows that the Rosenbrock method is by far superior.

Partial Differential Equations (acm G.1.8)
Stability and convergence of numerical methods (msc 65M12), Method of lines (msc 65M20), Finite difference methods (msc 65M06)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Lanser, D, Blom, J.G, & Verwer, J.G. (2000). Time integration of the shallow water equations in spherical geometry. Modelling, Analysis and Simulation [MAS]. CWI.