Abstract. Air pollution models can efficiently be used in different environmental studies. The atmosphere is the most dynamic component of the environment, where the pollutants can be transported over very long distances. Therefore the models must be defined on a large space domain. Moreover, all relevant physical and chemical processes must be adequately described. This leads to huge computational tasks. That is why it is difficult to handle numerically such models even on the most powerful up-to-date supercomputers. The particular model used in this study is the Danish Eulerian Model. The numerical methods used in the advection-diffusion part of this model consist of finite elements (for discretizing the spatial derivatives) followed by predictor-corrector schemes with several different correctors (in the numerical treatment of the resulting systems of ordinary differential equations). Implicit methods for the solution of stiff systems of ordinary differential equations are u...