For a long time operator splitting was the only computationally feasible way of implicit time integration in large scale Air Pollution Models. A recently proposed attractive alternative is Rosenbrock schemes combined with Approximate Matrix Factorization (AMF). With AMF, linear systems arising in implicit time stepping are solved approximately in such a way that the overall computational costs per time step are not higher than those of splitting methods. We propose and discuss two new variants of AMF. The first one is aimed at yet a further reduction of costs as compared with conventional AMF. The second variant of AMF provides in certain circumstances a better approximation to the inverse of the linear system matrix than standard AMF and requires the same computational work.

Partial Differential Equations (acm G.1.8), Numerical Linear Algebra (acm G.1.3), PHYSICAL SCIENCES AND ENGINEERING (acm J.2)
Stability and convergence of numerical methods (msc 65M12), Other matrix algorithms (msc 65F30), Method of lines (msc 65M20), Finite difference methods (msc 65M06)
Modelling, Analysis and Simulation [MAS]
Modelling, Analysis and Computation

Botchev, M.A, & Verwer, J.G. (2000). Improving approximate matrix factorizations for implicit time integration in air pollution modelling. Modelling, Analysis and Simulation [MAS]. CWI.