Eulerian and Semi-Lagrangian schemes based on commutator free exponential integrators

We consider commutator free exponential integrators combined with splitting and applied to convection diffusion problems semidiscretized in space. Numerical results show improved accuracy of the new approach compared to other methods. Numerical dispersion is however experienced due to the classical Eulerian formulation of the problem. A semi-Lagrangian approach is then proposed to take care of this drawback.